1 / | | 1 | ------------ dx | 3 + 4*sin(x) | / 0
Integral(1/(3 + 4*sin(x)), (x, 0, 1))
/ ___ \ / ___ \ / ___ |4 \/ 7 /x\| ___ |4 \/ 7 /x\| | \/ 7 *log|- + ----- + tan|-|| \/ 7 *log|- - ----- + tan|-|| | 1 \3 3 \2// \3 3 \2// | ------------ dx = C - ----------------------------- + ----------------------------- | 3 + 4*sin(x) 7 7 | /
/ ___\ / ___ \ / ___\ / ___ \ ___ |4 \/ 7 | ___ |4 \/ 7 | ___ |4 \/ 7 | ___ |4 \/ 7 | \/ 7 *log|- - -----| \/ 7 *log|- + ----- + tan(1/2)| \/ 7 *log|- + -----| \/ 7 *log|- - ----- + tan(1/2)| \3 3 / \3 3 / \3 3 / \3 3 / - -------------------- - ------------------------------- + -------------------- + ------------------------------- 7 7 7 7
=
/ ___\ / ___ \ / ___\ / ___ \ ___ |4 \/ 7 | ___ |4 \/ 7 | ___ |4 \/ 7 | ___ |4 \/ 7 | \/ 7 *log|- - -----| \/ 7 *log|- + ----- + tan(1/2)| \/ 7 *log|- + -----| \/ 7 *log|- - ----- + tan(1/2)| \3 3 / \3 3 / \3 3 / \3 3 / - -------------------- - ------------------------------- + -------------------- + ------------------------------- 7 7 7 7
-sqrt(7)*log(4/3 - sqrt(7)/3)/7 - sqrt(7)*log(4/3 + sqrt(7)/3 + tan(1/2))/7 + sqrt(7)*log(4/3 + sqrt(7)/3)/7 + sqrt(7)*log(4/3 - sqrt(7)/3 + tan(1/2))/7
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.