1 / | | 2 | 2*x + 3*x | ---------- dx | 4 | 16*x + 1 | / 0
Integral((2*x^2 + 3*x)/(16*x^4 + 1), (x, 0, 1))
/ / ___\ / ___\ | ___ |1 2 x*\/ 2 | ___ |1 2 x*\/ 2 | | 2 / 2\ \/ 2 *log|- + x + -------| ___ / ___\ ___ / ___\ \/ 2 *log|- + x - -------| | 2*x + 3*x 3*atan\4*x / \4 2 / \/ 2 *atan\1 + 2*x*\/ 2 / \/ 2 *atan\-1 + 2*x*\/ 2 / \4 2 / | ---------- dx = C + ------------ - --------------------------- + ------------------------- + -------------------------- + --------------------------- | 4 8 32 16 16 32 | 16*x + 1 | /
/ ______________ ______________\ / ______________ ______________\ / ______________ ______________\ / ______________ ______________\ _________________________ _________________________ _________________________ _________________________ | ___ / ___ ___ / ___ | | ___ / ___ ___ / ___ | | / ___ ___ ___ / ___ | | / ___ ___ ___ / ___ | / ______________ / ______________ ______________ \ / ______________ / ______________ ______________ \ / ______________ / ______________ ______________ \ / ______________ / ______________ ______________ \ ___ |31067 9765*\/ 2 12613*\/ 19 - 6*\/ 2 1221*\/ 2 *\/ 19 - 6*\/ 2 | ___ |115047 9119*\/ 2 57155*\/ 19 + 6*\/ 2 717*\/ 2 *\/ 19 + 6*\/ 2 | ___ |31067 12613*\/ 19 + 6*\/ 2 9765*\/ 2 1221*\/ 2 *\/ 19 + 6*\/ 2 | ___ |115047 57155*\/ 19 - 6*\/ 2 9119*\/ 2 717*\/ 2 *\/ 19 - 6*\/ 2 | / / ___ | ___ / ___ ___ / ___ | / / ___ | ___ / ___ ___ / ___ | / / ___ | ___ / ___ ___ / ___ | / / ___ | / ___ ___ ___ / ___ | \/ 2 *log|------ - ---------- + ----------------------- - ----------------------------| \/ 2 *log|------ + ---------- + ----------------------- + ---------------------------| \/ 2 *log|------ - ----------------------- + ---------- - ----------------------------| \/ 2 *log|------ - ----------------------- - ---------- + ---------------------------| / 21 \/ 19 + 6*\/ 2 | 1166 4*\/ 2 108*\/ 19 + 6*\/ 2 3*\/ 2 *\/ 19 + 6*\/ 2 | / 21 \/ 19 + 6*\/ 2 | 126 4*\/ 2 108*\/ 19 + 6*\/ 2 3*\/ 2 *\/ 19 + 6*\/ 2 | / 21 \/ 19 - 6*\/ 2 | 126 4*\/ 2 108*\/ 19 - 6*\/ 2 3*\/ 2 *\/ 19 - 6*\/ 2 | / 21 \/ 19 - 6*\/ 2 | 1166 108*\/ 19 - 6*\/ 2 4*\/ 2 3*\/ 2 *\/ 19 - 6*\/ 2 | \104329 104329 417316 417316 / \104329 104329 417316 417316 / \104329 417316 104329 417316 / \104329 417316 104329 417316 / - 2* / --- - ----------------- *atan|------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------| + 2* / --- - ----------------- *atan|- ------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------| + 2* / --- + ----------------- *atan|------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------| + 2* / --- + ----------------- *atan|------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------| - --------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------- \/ 512 256 | __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________| \/ 512 256 | __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________| \/ 512 256 | __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________| \/ 512 256 | __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________| 32 32 32 32 | / ______________ / ______________ ______________ / ______________ / ______________ / ______________ ______________ / ______________ / ______________ / ______________ ______________ / ______________ / ______________ / ______________ ______________ / ______________ | | / ______________ / ______________ ______________ / ______________ / ______________ / ______________ ______________ / ______________ / ______________ / ______________ ______________ / ______________ / ______________ / ______________ ______________ / ______________ | | / ______________ / ______________ ______________ / ______________ / ______________ / ______________ ______________ / ______________ / ______________ / ______________ ______________ / ______________ / ______________ / ______________ ______________ / ______________ | | / ______________ / ______________ ______________ / ______________ / ______________ / ______________ ______________ / ______________ / ______________ / ______________ ______________ / ______________ / ______________ / ______________ ______________ / ______________ | | / / ___ ___ / / ___ ___ / ___ / / ___ / / ___ ___ / / ___ ___ / ___ / / ___ / / ___ ___ / / ___ ___ / ___ / / ___ / / ___ ___ / / ___ ___ / ___ / / ___ | | / / ___ ___ / / ___ ___ / ___ / / ___ / / ___ ___ / / ___ ___ / ___ / / ___ / / ___ ___ / / ___ ___ / ___ / / ___ / / ___ ___ / / ___ ___ / ___ / / ___ | | / / ___ ___ / / ___ ___ / ___ / / ___ / / ___ ___ / / ___ ___ / ___ / / ___ / / ___ ___ / / ___ ___ / ___ / / ___ / / ___ ___ / / ___ ___ / ___ / / ___ | | / / ___ ___ / / ___ ___ / ___ / / ___ / / ___ ___ / / ___ ___ / ___ / / ___ / / ___ ___ / / ___ ___ / ___ / / ___ / / ___ ___ / / ___ ___ / ___ / / ___ | \108*\/ 21 - 2*\/ 19 + 6*\/ 2 + 18*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 + \/ 2 *\/ 19 + 6*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 108*\/ 21 - 2*\/ 19 + 6*\/ 2 + 18*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 + \/ 2 *\/ 19 + 6*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 108*\/ 21 - 2*\/ 19 + 6*\/ 2 + 18*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 + \/ 2 *\/ 19 + 6*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 108*\/ 21 - 2*\/ 19 + 6*\/ 2 + 18*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 + \/ 2 *\/ 19 + 6*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 / \ 108*\/ 21 - 2*\/ 19 + 6*\/ 2 + 18*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 + \/ 2 *\/ 19 + 6*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 108*\/ 21 - 2*\/ 19 + 6*\/ 2 + 18*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 + \/ 2 *\/ 19 + 6*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 108*\/ 21 - 2*\/ 19 + 6*\/ 2 + 18*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 + \/ 2 *\/ 19 + 6*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 108*\/ 21 - 2*\/ 19 + 6*\/ 2 + 18*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 + \/ 2 *\/ 19 + 6*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 / \108*\/ 21 + 2*\/ 19 - 6*\/ 2 - 18*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 + \/ 2 *\/ 19 - 6*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 108*\/ 21 + 2*\/ 19 - 6*\/ 2 - 18*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 + \/ 2 *\/ 19 - 6*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 108*\/ 21 + 2*\/ 19 - 6*\/ 2 - 18*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 + \/ 2 *\/ 19 - 6*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 108*\/ 21 + 2*\/ 19 - 6*\/ 2 - 18*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 + \/ 2 *\/ 19 - 6*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 / \108*\/ 21 + 2*\/ 19 - 6*\/ 2 - 18*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 + \/ 2 *\/ 19 - 6*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 108*\/ 21 + 2*\/ 19 - 6*\/ 2 - 18*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 + \/ 2 *\/ 19 - 6*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 108*\/ 21 + 2*\/ 19 - 6*\/ 2 - 18*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 + \/ 2 *\/ 19 - 6*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 108*\/ 21 + 2*\/ 19 - 6*\/ 2 - 18*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 + \/ 2 *\/ 19 - 6*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 /
=
/ ______________ ______________\ / ______________ ______________\ / ______________ ______________\ / ______________ ______________\ _________________________ _________________________ _________________________ _________________________ | ___ / ___ ___ / ___ | | ___ / ___ ___ / ___ | | / ___ ___ ___ / ___ | | / ___ ___ ___ / ___ | / ______________ / ______________ ______________ \ / ______________ / ______________ ______________ \ / ______________ / ______________ ______________ \ / ______________ / ______________ ______________ \ ___ |31067 9765*\/ 2 12613*\/ 19 - 6*\/ 2 1221*\/ 2 *\/ 19 - 6*\/ 2 | ___ |115047 9119*\/ 2 57155*\/ 19 + 6*\/ 2 717*\/ 2 *\/ 19 + 6*\/ 2 | ___ |31067 12613*\/ 19 + 6*\/ 2 9765*\/ 2 1221*\/ 2 *\/ 19 + 6*\/ 2 | ___ |115047 57155*\/ 19 - 6*\/ 2 9119*\/ 2 717*\/ 2 *\/ 19 - 6*\/ 2 | / / ___ | ___ / ___ ___ / ___ | / / ___ | ___ / ___ ___ / ___ | / / ___ | ___ / ___ ___ / ___ | / / ___ | / ___ ___ ___ / ___ | \/ 2 *log|------ - ---------- + ----------------------- - ----------------------------| \/ 2 *log|------ + ---------- + ----------------------- + ---------------------------| \/ 2 *log|------ - ----------------------- + ---------- - ----------------------------| \/ 2 *log|------ - ----------------------- - ---------- + ---------------------------| / 21 \/ 19 + 6*\/ 2 | 1166 4*\/ 2 108*\/ 19 + 6*\/ 2 3*\/ 2 *\/ 19 + 6*\/ 2 | / 21 \/ 19 + 6*\/ 2 | 126 4*\/ 2 108*\/ 19 + 6*\/ 2 3*\/ 2 *\/ 19 + 6*\/ 2 | / 21 \/ 19 - 6*\/ 2 | 126 4*\/ 2 108*\/ 19 - 6*\/ 2 3*\/ 2 *\/ 19 - 6*\/ 2 | / 21 \/ 19 - 6*\/ 2 | 1166 108*\/ 19 - 6*\/ 2 4*\/ 2 3*\/ 2 *\/ 19 - 6*\/ 2 | \104329 104329 417316 417316 / \104329 104329 417316 417316 / \104329 417316 104329 417316 / \104329 417316 104329 417316 / - 2* / --- - ----------------- *atan|------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------| + 2* / --- - ----------------- *atan|- ------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------| + 2* / --- + ----------------- *atan|------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------| + 2* / --- + ----------------- *atan|------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------| - --------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------- \/ 512 256 | __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________| \/ 512 256 | __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________| \/ 512 256 | __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________| \/ 512 256 | __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________| 32 32 32 32 | / ______________ / ______________ ______________ / ______________ / ______________ / ______________ ______________ / ______________ / ______________ / ______________ ______________ / ______________ / ______________ / ______________ ______________ / ______________ | | / ______________ / ______________ ______________ / ______________ / ______________ / ______________ ______________ / ______________ / ______________ / ______________ ______________ / ______________ / ______________ / ______________ ______________ / ______________ | | / ______________ / ______________ ______________ / ______________ / ______________ / ______________ ______________ / ______________ / ______________ / ______________ ______________ / ______________ / ______________ / ______________ ______________ / ______________ | | / ______________ / ______________ ______________ / ______________ / ______________ / ______________ ______________ / ______________ / ______________ / ______________ ______________ / ______________ / ______________ / ______________ ______________ / ______________ | | / / ___ ___ / / ___ ___ / ___ / / ___ / / ___ ___ / / ___ ___ / ___ / / ___ / / ___ ___ / / ___ ___ / ___ / / ___ / / ___ ___ / / ___ ___ / ___ / / ___ | | / / ___ ___ / / ___ ___ / ___ / / ___ / / ___ ___ / / ___ ___ / ___ / / ___ / / ___ ___ / / ___ ___ / ___ / / ___ / / ___ ___ / / ___ ___ / ___ / / ___ | | / / ___ ___ / / ___ ___ / ___ / / ___ / / ___ ___ / / ___ ___ / ___ / / ___ / / ___ ___ / / ___ ___ / ___ / / ___ / / ___ ___ / / ___ ___ / ___ / / ___ | | / / ___ ___ / / ___ ___ / ___ / / ___ / / ___ ___ / / ___ ___ / ___ / / ___ / / ___ ___ / / ___ ___ / ___ / / ___ / / ___ ___ / / ___ ___ / ___ / / ___ | \108*\/ 21 - 2*\/ 19 + 6*\/ 2 + 18*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 + \/ 2 *\/ 19 + 6*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 108*\/ 21 - 2*\/ 19 + 6*\/ 2 + 18*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 + \/ 2 *\/ 19 + 6*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 108*\/ 21 - 2*\/ 19 + 6*\/ 2 + 18*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 + \/ 2 *\/ 19 + 6*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 108*\/ 21 - 2*\/ 19 + 6*\/ 2 + 18*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 + \/ 2 *\/ 19 + 6*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 / \ 108*\/ 21 - 2*\/ 19 + 6*\/ 2 + 18*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 + \/ 2 *\/ 19 + 6*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 108*\/ 21 - 2*\/ 19 + 6*\/ 2 + 18*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 + \/ 2 *\/ 19 + 6*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 108*\/ 21 - 2*\/ 19 + 6*\/ 2 + 18*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 + \/ 2 *\/ 19 + 6*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 108*\/ 21 - 2*\/ 19 + 6*\/ 2 + 18*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 + \/ 2 *\/ 19 + 6*\/ 2 *\/ 21 - 2*\/ 19 + 6*\/ 2 / \108*\/ 21 + 2*\/ 19 - 6*\/ 2 - 18*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 + \/ 2 *\/ 19 - 6*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 108*\/ 21 + 2*\/ 19 - 6*\/ 2 - 18*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 + \/ 2 *\/ 19 - 6*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 108*\/ 21 + 2*\/ 19 - 6*\/ 2 - 18*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 + \/ 2 *\/ 19 - 6*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 108*\/ 21 + 2*\/ 19 - 6*\/ 2 - 18*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 + \/ 2 *\/ 19 - 6*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 / \108*\/ 21 + 2*\/ 19 - 6*\/ 2 - 18*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 + \/ 2 *\/ 19 - 6*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 108*\/ 21 + 2*\/ 19 - 6*\/ 2 - 18*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 + \/ 2 *\/ 19 - 6*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 108*\/ 21 + 2*\/ 19 - 6*\/ 2 - 18*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 + \/ 2 *\/ 19 - 6*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 108*\/ 21 + 2*\/ 19 - 6*\/ 2 - 18*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 + \/ 2 *\/ 19 - 6*\/ 2 *\/ 21 + 2*\/ 19 - 6*\/ 2 /
-2*sqrt(21/512 - sqrt(19 + 6*sqrt(2))/256)*atan(1166/(108*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + 18*sqrt(2)*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + sqrt(2)*sqrt(19 + 6*sqrt(2))*sqrt(21 - 2*sqrt(19 + 6*sqrt(2)))) - 4*sqrt(2)/(108*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + 18*sqrt(2)*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + sqrt(2)*sqrt(19 + 6*sqrt(2))*sqrt(21 - 2*sqrt(19 + 6*sqrt(2)))) + 108*sqrt(19 + 6*sqrt(2))/(108*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + 18*sqrt(2)*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + sqrt(2)*sqrt(19 + 6*sqrt(2))*sqrt(21 - 2*sqrt(19 + 6*sqrt(2)))) + 3*sqrt(2)*sqrt(19 + 6*sqrt(2))/(108*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + 18*sqrt(2)*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + sqrt(2)*sqrt(19 + 6*sqrt(2))*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))))) + 2*sqrt(21/512 - sqrt(19 + 6*sqrt(2))/256)*atan(-126/(108*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + 18*sqrt(2)*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + sqrt(2)*sqrt(19 + 6*sqrt(2))*sqrt(21 - 2*sqrt(19 + 6*sqrt(2)))) - 4*sqrt(2)/(108*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + 18*sqrt(2)*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + sqrt(2)*sqrt(19 + 6*sqrt(2))*sqrt(21 - 2*sqrt(19 + 6*sqrt(2)))) + 108*sqrt(19 + 6*sqrt(2))/(108*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + 18*sqrt(2)*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + sqrt(2)*sqrt(19 + 6*sqrt(2))*sqrt(21 - 2*sqrt(19 + 6*sqrt(2)))) + 3*sqrt(2)*sqrt(19 + 6*sqrt(2))/(108*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + 18*sqrt(2)*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))) + sqrt(2)*sqrt(19 + 6*sqrt(2))*sqrt(21 - 2*sqrt(19 + 6*sqrt(2))))) + 2*sqrt(21/512 + sqrt(19 - 6*sqrt(2))/256)*atan(126/(108*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) - 18*sqrt(2)*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) + sqrt(2)*sqrt(19 - 6*sqrt(2))*sqrt(21 + 2*sqrt(19 - 6*sqrt(2)))) - 4*sqrt(2)/(108*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) - 18*sqrt(2)*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) + sqrt(2)*sqrt(19 - 6*sqrt(2))*sqrt(21 + 2*sqrt(19 - 6*sqrt(2)))) + 108*sqrt(19 - 6*sqrt(2))/(108*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) - 18*sqrt(2)*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) + sqrt(2)*sqrt(19 - 6*sqrt(2))*sqrt(21 + 2*sqrt(19 - 6*sqrt(2)))) - 3*sqrt(2)*sqrt(19 - 6*sqrt(2))/(108*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) - 18*sqrt(2)*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) + sqrt(2)*sqrt(19 - 6*sqrt(2))*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))))) + 2*sqrt(21/512 + sqrt(19 - 6*sqrt(2))/256)*atan(1166/(108*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) - 18*sqrt(2)*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) + sqrt(2)*sqrt(19 - 6*sqrt(2))*sqrt(21 + 2*sqrt(19 - 6*sqrt(2)))) - 108*sqrt(19 - 6*sqrt(2))/(108*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) - 18*sqrt(2)*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) + sqrt(2)*sqrt(19 - 6*sqrt(2))*sqrt(21 + 2*sqrt(19 - 6*sqrt(2)))) + 4*sqrt(2)/(108*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) - 18*sqrt(2)*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) + sqrt(2)*sqrt(19 - 6*sqrt(2))*sqrt(21 + 2*sqrt(19 - 6*sqrt(2)))) + 3*sqrt(2)*sqrt(19 - 6*sqrt(2))/(108*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) - 18*sqrt(2)*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))) + sqrt(2)*sqrt(19 - 6*sqrt(2))*sqrt(21 + 2*sqrt(19 - 6*sqrt(2))))) - sqrt(2)*log(31067/104329 - 9765*sqrt(2)/104329 + 12613*sqrt(19 - 6*sqrt(2))/417316 - 1221*sqrt(2)*sqrt(19 - 6*sqrt(2))/417316)/32 - sqrt(2)*log(115047/104329 + 9119*sqrt(2)/104329 + 57155*sqrt(19 + 6*sqrt(2))/417316 + 717*sqrt(2)*sqrt(19 + 6*sqrt(2))/417316)/32 + sqrt(2)*log(31067/104329 - 12613*sqrt(19 + 6*sqrt(2))/417316 + 9765*sqrt(2)/104329 - 1221*sqrt(2)*sqrt(19 + 6*sqrt(2))/417316)/32 + sqrt(2)*log(115047/104329 - 57155*sqrt(19 - 6*sqrt(2))/417316 - 9119*sqrt(2)/104329 + 717*sqrt(2)*sqrt(19 - 6*sqrt(2))/417316)/32
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.