Sr Examen
Integral de ln((x+1)^1/2-1) dx
Solución
Ha introducido
[src]
1 / | | / _______ \ | log\\/ x + 1 - 1/ dx | / 0
$$\int\limits_{0}^{1} \log{\left(\sqrt{x + 1} - 1 \right)}\, dx$$
Integral(log(sqrt(x + 1) - 1), (x, 0, 1))
Respuesta (Indefinida)
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/ | | / _______ \ 1 _______ x / _______ \ | log\\/ x + 1 - 1/ dx = - - + C - \/ x + 1 - - + x*log\\/ x + 1 - 1/ | 2 2 /
$$\int \log{\left(\sqrt{x + 1} - 1 \right)}\, dx = C + x \log{\left(\sqrt{x + 1} - 1 \right)} - \frac{x}{2} - \sqrt{x + 1} - \frac{1}{2}$$
Respuesta
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__1, 1 /1 2 | \ __0, 2 /2, 1 | \ ___ __1, 1 /1 2 | \ ___ __0, 2 /2, 1 | \
___ / ___\ ___ / ___\ ___ 64*pi*I*/__ | | 2| 64*pi*I*/__ | | 2| 32*pi*I*\/ 2 */__ | | 2| 32*pi*I*\/ 2 */__ | | 2|
3 32*\/ 2 64*log\-1 + \/ 2 / __1, 1 /1 2 | \ __0, 2 /2, 1 | \ 64*pi*I 32*\/ 2 *log\-1 + \/ 2 / 32*pi*I*\/ 2 \_|2, 2 \1 0 | / \_|2, 2 \ 1, 0 | / \_|2, 2 \1 0 | / \_|2, 2 \ 1, 0 | /
- - ------------- + ------------------ - pi*I*/__ | | 1| - pi*I*/__ | | 1| - ------------- - ------------------------ + ------------- + -------------------------- + -------------------------------- - -------------------------------- - --------------------------------------
2 ___ ___ \_|2, 2 \1 0 | / \_|2, 2 \ 1, 0 | / ___ ___ ___ ___ ___ ___ ___
64 - 32*\/ 2 64 - 32*\/ 2 64 - 32*\/ 2 64 - 32*\/ 2 64 - 32*\/ 2 64 - 32*\/ 2 64 - 32*\/ 2 64 - 32*\/ 2 64 - 32*\/ 2
$$\frac{64 \log{\left(-1 + \sqrt{2} \right)}}{64 - 32 \sqrt{2}} - \frac{32 \sqrt{2}}{64 - 32 \sqrt{2}} - i \pi {G_{2, 2}^{0, 2}\left(\begin{matrix} 2, 1 & \\ & 1, 0 \end{matrix} \middle| {1} \right)} + \frac{3}{2} - \frac{32 \sqrt{2} \log{\left(-1 + \sqrt{2} \right)}}{64 - 32 \sqrt{2}} - \frac{64 i \pi}{64 - 32 \sqrt{2}} - \frac{32 \sqrt{2} i \pi {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & 2 \\1 & 0 \end{matrix} \middle| {2} \right)}}{64 - 32 \sqrt{2}} - \frac{32 \sqrt{2} i \pi {G_{2, 2}^{0, 2}\left(\begin{matrix} 2, 1 & \\ & 1, 0 \end{matrix} \middle| {2} \right)}}{64 - 32 \sqrt{2}} - i \pi {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & 2 \\1 & 0 \end{matrix} \middle| {1} \right)} + \frac{32 \sqrt{2} i \pi}{64 - 32 \sqrt{2}} + \frac{64 i \pi {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & 2 \\1 & 0 \end{matrix} \middle| {2} \right)}}{64 - 32 \sqrt{2}} + \frac{64 i \pi {G_{2, 2}^{0, 2}\left(\begin{matrix} 2, 1 & \\ & 1, 0 \end{matrix} \middle| {2} \right)}}{64 - 32 \sqrt{2}}$$
=
=
__1, 1 /1 2 | \ __0, 2 /2, 1 | \ ___ __1, 1 /1 2 | \ ___ __0, 2 /2, 1 | \
___ / ___\ ___ / ___\ ___ 64*pi*I*/__ | | 2| 64*pi*I*/__ | | 2| 32*pi*I*\/ 2 */__ | | 2| 32*pi*I*\/ 2 */__ | | 2|
3 32*\/ 2 64*log\-1 + \/ 2 / __1, 1 /1 2 | \ __0, 2 /2, 1 | \ 64*pi*I 32*\/ 2 *log\-1 + \/ 2 / 32*pi*I*\/ 2 \_|2, 2 \1 0 | / \_|2, 2 \ 1, 0 | / \_|2, 2 \1 0 | / \_|2, 2 \ 1, 0 | /
- - ------------- + ------------------ - pi*I*/__ | | 1| - pi*I*/__ | | 1| - ------------- - ------------------------ + ------------- + -------------------------- + -------------------------------- - -------------------------------- - --------------------------------------
2 ___ ___ \_|2, 2 \1 0 | / \_|2, 2 \ 1, 0 | / ___ ___ ___ ___ ___ ___ ___
64 - 32*\/ 2 64 - 32*\/ 2 64 - 32*\/ 2 64 - 32*\/ 2 64 - 32*\/ 2 64 - 32*\/ 2 64 - 32*\/ 2 64 - 32*\/ 2 64 - 32*\/ 2
$$\frac{64 \log{\left(-1 + \sqrt{2} \right)}}{64 - 32 \sqrt{2}} - \frac{32 \sqrt{2}}{64 - 32 \sqrt{2}} - i \pi {G_{2, 2}^{0, 2}\left(\begin{matrix} 2, 1 & \\ & 1, 0 \end{matrix} \middle| {1} \right)} + \frac{3}{2} - \frac{32 \sqrt{2} \log{\left(-1 + \sqrt{2} \right)}}{64 - 32 \sqrt{2}} - \frac{64 i \pi}{64 - 32 \sqrt{2}} - \frac{32 \sqrt{2} i \pi {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & 2 \\1 & 0 \end{matrix} \middle| {2} \right)}}{64 - 32 \sqrt{2}} - \frac{32 \sqrt{2} i \pi {G_{2, 2}^{0, 2}\left(\begin{matrix} 2, 1 & \\ & 1, 0 \end{matrix} \middle| {2} \right)}}{64 - 32 \sqrt{2}} - i \pi {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & 2 \\1 & 0 \end{matrix} \middle| {1} \right)} + \frac{32 \sqrt{2} i \pi}{64 - 32 \sqrt{2}} + \frac{64 i \pi {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & 2 \\1 & 0 \end{matrix} \middle| {2} \right)}}{64 - 32 \sqrt{2}} + \frac{64 i \pi {G_{2, 2}^{0, 2}\left(\begin{matrix} 2, 1 & \\ & 1, 0 \end{matrix} \middle| {2} \right)}}{64 - 32 \sqrt{2}}$$
3/2 - 32*sqrt(2)/(64 - 32*sqrt(2)) + 64*log(-1 + sqrt(2))/(64 - 32*sqrt(2)) - pi*i*meijerg(((1,), (2,)), ((1,), (0,)), 1) - pi*i*meijerg(((2, 1), ()), ((), (1, 0)), 1) - 64*pi*i/(64 - 32*sqrt(2)) - 32*sqrt(2)*log(-1 + sqrt(2))/(64 - 32*sqrt(2)) + 32*pi*i*sqrt(2)/(64 - 32*sqrt(2)) + 64*pi*i*meijerg(((1,), (2,)), ((1,), (0,)), 2)/(64 - 32*sqrt(2)) + 64*pi*i*meijerg(((2, 1), ()), ((), (1, 0)), 2)/(64 - 32*sqrt(2)) - 32*pi*i*sqrt(2)*meijerg(((1,), (2,)), ((1,), (0,)), 2)/(64 - 32*sqrt(2)) - 32*pi*i*sqrt(2)*meijerg(((2, 1), ()), ((), (1, 0)), 2)/(64 - 32*sqrt(2))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.