Sr Examen
Integral de sqrt(X+1)*ln(X+3) dx
Solución
Ha introducido
[src]
1 / | | _______ | \/ x + 1 *log(x + 3) dx | / 1/10
$$\int\limits_{\frac{1}{10}}^{1} \sqrt{x + 1} \log{\left(x + 3 \right)}\, dx$$
Integral(sqrt(x + 1)*log(x + 3), (x, 1/10, 1))
Respuesta (Indefinida)
[src]
/ ___ _______\ / ___ |\/ 2 *\/ 1 + x | | 3/2 _______ 8*\/ 2 *atan|---------------| 3/2 | _______ 4*(1 + x) 8*\/ 1 + x \ 2 / 2*(1 + x) *log(3 + x) | \/ x + 1 *log(x + 3) dx = C - ------------ + ----------- - ----------------------------- + ----------------------- | 9 3 3 3 /
$$\int \sqrt{x + 1} \log{\left(x + 3 \right)}\, dx = C + \frac{2 \left(x + 1\right)^{\frac{3}{2}} \log{\left(x + 3 \right)}}{3} - \frac{4 \left(x + 1\right)^{\frac{3}{2}}}{9} + \frac{8 \sqrt{x + 1}}{3} - \frac{8 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{3}$$
Gráfica
Respuesta
[src]
/ ____\
_____ /31\ ___ |\/ 55 |
_____ ___ 11*\/ 110 *log|--| ___ ___ 8*\/ 2 *atan|------|
49*\/ 110 16*\/ 2 __1, 1 / 1 5/2 | \ __0, 2 /5/2, 1 | \ __1, 1 / 1 5/2 | 11\ __0, 2 /5/2, 1 | 11\ \20/ 2*pi*\/ 2 4*\/ 2 *log(2) \ 10 /
- ---------- + -------- + log(2)*/__ | | 2| + log(2)*/__ | | 2| - log(2)*/__ | | --| - log(2)*/__ | | --| - ------------------ - ---------- + -------------- + --------------------
225 9 \_|2, 2 \3/2 0 | / \_|2, 2 \ 3/2, 0 | / \_|2, 2 \3/2 0 | 10/ \_|2, 2 \ 3/2, 0 | 10/ 150 3 3 3
$$- \frac{2 \sqrt{2} \pi}{3} - \frac{49 \sqrt{110}}{225} - {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{5}{2} \\\frac{3}{2} & 0 \end{matrix} \middle| {\frac{11}{10}} \right)} \log{\left(2 \right)} - \frac{11 \sqrt{110} \log{\left(\frac{31}{20} \right)}}{150} - {G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{5}{2}, 1 & \\ & \frac{3}{2}, 0 \end{matrix} \middle| {\frac{11}{10}} \right)} \log{\left(2 \right)} + {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{5}{2} \\\frac{3}{2} & 0 \end{matrix} \middle| {2} \right)} \log{\left(2 \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{5}{2}, 1 & \\ & \frac{3}{2}, 0 \end{matrix} \middle| {2} \right)} \log{\left(2 \right)} + \frac{4 \sqrt{2} \log{\left(2 \right)}}{3} + \frac{8 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{55}}{10} \right)}}{3} + \frac{16 \sqrt{2}}{9}$$
=
=
/ ____\
_____ /31\ ___ |\/ 55 |
_____ ___ 11*\/ 110 *log|--| ___ ___ 8*\/ 2 *atan|------|
49*\/ 110 16*\/ 2 __1, 1 / 1 5/2 | \ __0, 2 /5/2, 1 | \ __1, 1 / 1 5/2 | 11\ __0, 2 /5/2, 1 | 11\ \20/ 2*pi*\/ 2 4*\/ 2 *log(2) \ 10 /
- ---------- + -------- + log(2)*/__ | | 2| + log(2)*/__ | | 2| - log(2)*/__ | | --| - log(2)*/__ | | --| - ------------------ - ---------- + -------------- + --------------------
225 9 \_|2, 2 \3/2 0 | / \_|2, 2 \ 3/2, 0 | / \_|2, 2 \3/2 0 | 10/ \_|2, 2 \ 3/2, 0 | 10/ 150 3 3 3
$$- \frac{2 \sqrt{2} \pi}{3} - \frac{49 \sqrt{110}}{225} - {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{5}{2} \\\frac{3}{2} & 0 \end{matrix} \middle| {\frac{11}{10}} \right)} \log{\left(2 \right)} - \frac{11 \sqrt{110} \log{\left(\frac{31}{20} \right)}}{150} - {G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{5}{2}, 1 & \\ & \frac{3}{2}, 0 \end{matrix} \middle| {\frac{11}{10}} \right)} \log{\left(2 \right)} + {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{5}{2} \\\frac{3}{2} & 0 \end{matrix} \middle| {2} \right)} \log{\left(2 \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{5}{2}, 1 & \\ & \frac{3}{2}, 0 \end{matrix} \middle| {2} \right)} \log{\left(2 \right)} + \frac{4 \sqrt{2} \log{\left(2 \right)}}{3} + \frac{8 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{55}}{10} \right)}}{3} + \frac{16 \sqrt{2}}{9}$$
-49*sqrt(110)/225 + 16*sqrt(2)/9 + log(2)*meijerg(((1,), (5/2,)), ((3/2,), (0,)), 2) + log(2)*meijerg(((5/2, 1), ()), ((), (3/2, 0)), 2) - log(2)*meijerg(((1,), (5/2,)), ((3/2,), (0,)), 11/10) - log(2)*meijerg(((5/2, 1), ()), ((), (3/2, 0)), 11/10) - 11*sqrt(110)*log(31/20)/150 - 2*pi*sqrt(2)/3 + 4*sqrt(2)*log(2)/3 + 8*sqrt(2)*atan(sqrt(55)/10)/3
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.