Sr Examen
Integral de sin/(x+5)^(1/3) dx
Solución
Ha introducido
[src]
oo / | | sin(x) | --------- dx | 3 _______ | \/ x + 5 | / 2
$$\int\limits_{2}^{\infty} \frac{\sin{\left(x \right)}}{\sqrt[3]{x + 5}}\, dx$$
Integral(sin(x)/(x + 5)^(1/3), (x, 2, oo))
Respuesta (Indefinida)
[src]
/ / | | | sin(x) | sin(x) | --------- dx = C + | --------- dx | 3 _______ | 3 _______ | \/ x + 5 | \/ 5 + x | | / /
$$\int \frac{\sin{\left(x \right)}}{\sqrt[3]{x + 5}}\, dx = C + \int \frac{\sin{\left(x \right)}}{\sqrt[3]{x + 5}}\, dx$$
Respuesta
[src]
/ _ \ / _ \
| |_ / 1/3 | \ | | |_ / 5/6 | \ |
|Gamma(-1/3)* | | | -49/4| 2/3 3 ___ | |7*Gamma(-5/6)* | | | -49/4| 2/3 3 ___ |
/ _ \ / _ \ / _ \ / _ \ 2/3 ____ | 1 2 \1/2, 4/3 | / 2 *\/ 7 *Gamma(1/3)| 2/3 ____ | 1 2 \3/2, 11/6 | / 2 *\/ 7 *Gamma(5/6)|
| |_ / 5/6 | \ | | |_ / 1/3 | \ | | |_ / 5/6 | \ | | |_ / 1/3 | \ | 5*7 *\/ pi *|----------------------------------- + ---------------------|*sin(1) 5*7 *\/ pi *|-------------------------------------- + ---------------------|*cos(1)
|7*Gamma(-5/6)* | | | -49/4| 2/3 3 ___ | |Gamma(-1/3)* | | | -49/4| 2/3 3 ___ | |7*Gamma(-5/6)* | | | -49/4| 2/3 3 ___ | |Gamma(-1/3)* | | | -49/4| 2/3 3 ___ | | ____ 7*Gamma(1/6) | | ____ 7*Gamma(2/3) |
2/3 ____ 3 | 1 2 \3/2, 11/6 | / 2 *\/ 7 *Gamma(5/6)| 2/3 ____ 5 | 1 2 \1/2, 4/3 | / 2 *\/ 7 *Gamma(1/3)| 2/3 ____ 5 | 1 2 \3/2, 11/6 | / 2 *\/ 7 *Gamma(5/6)| 2/3 ____ 3 | 1 2 \1/2, 4/3 | / 2 *\/ 7 *Gamma(1/3)| \ \/ pi *Gamma(2/3) / \ \/ pi *Gamma(1/6) /
- 10*7 *\/ pi *cos (1)*|-------------------------------------- + ---------------------| - 8*7 *\/ pi *sin (1)*|----------------------------------- + ---------------------| + 8*7 *\/ pi *cos (1)*|-------------------------------------- + ---------------------| + 10*7 *\/ pi *sin (1)*|----------------------------------- + ---------------------| - ---------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------
| ____ 7*Gamma(2/3) | | ____ 7*Gamma(1/6) | | ____ 7*Gamma(2/3) | | ____ 7*Gamma(1/6) | 2 2
\ \/ pi *Gamma(1/6) / \ \/ pi *Gamma(2/3) / \ \/ pi *Gamma(1/6) / \ \/ pi *Gamma(2/3) /
$$- 10 \cdot 7^{\frac{2}{3}} \sqrt{\pi} \left(\frac{7 \Gamma\left(- \frac{5}{6}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{5}{6} \\ \frac{3}{2}, \frac{11}{6} \end{matrix}\middle| {- \frac{49}{4}} \right)}}{\sqrt{\pi} \Gamma\left(\frac{1}{6}\right)} + \frac{2^{\frac{2}{3}} \sqrt[3]{7} \Gamma\left(\frac{5}{6}\right)}{7 \Gamma\left(\frac{2}{3}\right)}\right) \cos^{3}{\left(1 \right)} + 8 \cdot 7^{\frac{2}{3}} \sqrt{\pi} \left(\frac{7 \Gamma\left(- \frac{5}{6}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{5}{6} \\ \frac{3}{2}, \frac{11}{6} \end{matrix}\middle| {- \frac{49}{4}} \right)}}{\sqrt{\pi} \Gamma\left(\frac{1}{6}\right)} + \frac{2^{\frac{2}{3}} \sqrt[3]{7} \Gamma\left(\frac{5}{6}\right)}{7 \Gamma\left(\frac{2}{3}\right)}\right) \cos^{5}{\left(1 \right)} + \frac{5 \cdot 7^{\frac{2}{3}} \sqrt{\pi} \left(\frac{7 \Gamma\left(- \frac{5}{6}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{5}{6} \\ \frac{3}{2}, \frac{11}{6} \end{matrix}\middle| {- \frac{49}{4}} \right)}}{\sqrt{\pi} \Gamma\left(\frac{1}{6}\right)} + \frac{2^{\frac{2}{3}} \sqrt[3]{7} \Gamma\left(\frac{5}{6}\right)}{7 \Gamma\left(\frac{2}{3}\right)}\right) \cos{\left(1 \right)}}{2} - 8 \cdot 7^{\frac{2}{3}} \sqrt{\pi} \left(\frac{\Gamma\left(- \frac{1}{3}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{1}{3} \\ \frac{1}{2}, \frac{4}{3} \end{matrix}\middle| {- \frac{49}{4}} \right)}}{\sqrt{\pi} \Gamma\left(\frac{2}{3}\right)} + \frac{2^{\frac{2}{3}} \sqrt[3]{7} \Gamma\left(\frac{1}{3}\right)}{7 \Gamma\left(\frac{1}{6}\right)}\right) \sin^{5}{\left(1 \right)} - \frac{5 \cdot 7^{\frac{2}{3}} \sqrt{\pi} \left(\frac{\Gamma\left(- \frac{1}{3}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{1}{3} \\ \frac{1}{2}, \frac{4}{3} \end{matrix}\middle| {- \frac{49}{4}} \right)}}{\sqrt{\pi} \Gamma\left(\frac{2}{3}\right)} + \frac{2^{\frac{2}{3}} \sqrt[3]{7} \Gamma\left(\frac{1}{3}\right)}{7 \Gamma\left(\frac{1}{6}\right)}\right) \sin{\left(1 \right)}}{2} + 10 \cdot 7^{\frac{2}{3}} \sqrt{\pi} \left(\frac{\Gamma\left(- \frac{1}{3}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{1}{3} \\ \frac{1}{2}, \frac{4}{3} \end{matrix}\middle| {- \frac{49}{4}} \right)}}{\sqrt{\pi} \Gamma\left(\frac{2}{3}\right)} + \frac{2^{\frac{2}{3}} \sqrt[3]{7} \Gamma\left(\frac{1}{3}\right)}{7 \Gamma\left(\frac{1}{6}\right)}\right) \sin^{3}{\left(1 \right)}$$
=
=
/ _ \ / _ \
| |_ / 1/3 | \ | | |_ / 5/6 | \ |
|Gamma(-1/3)* | | | -49/4| 2/3 3 ___ | |7*Gamma(-5/6)* | | | -49/4| 2/3 3 ___ |
/ _ \ / _ \ / _ \ / _ \ 2/3 ____ | 1 2 \1/2, 4/3 | / 2 *\/ 7 *Gamma(1/3)| 2/3 ____ | 1 2 \3/2, 11/6 | / 2 *\/ 7 *Gamma(5/6)|
| |_ / 5/6 | \ | | |_ / 1/3 | \ | | |_ / 5/6 | \ | | |_ / 1/3 | \ | 5*7 *\/ pi *|----------------------------------- + ---------------------|*sin(1) 5*7 *\/ pi *|-------------------------------------- + ---------------------|*cos(1)
|7*Gamma(-5/6)* | | | -49/4| 2/3 3 ___ | |Gamma(-1/3)* | | | -49/4| 2/3 3 ___ | |7*Gamma(-5/6)* | | | -49/4| 2/3 3 ___ | |Gamma(-1/3)* | | | -49/4| 2/3 3 ___ | | ____ 7*Gamma(1/6) | | ____ 7*Gamma(2/3) |
2/3 ____ 3 | 1 2 \3/2, 11/6 | / 2 *\/ 7 *Gamma(5/6)| 2/3 ____ 5 | 1 2 \1/2, 4/3 | / 2 *\/ 7 *Gamma(1/3)| 2/3 ____ 5 | 1 2 \3/2, 11/6 | / 2 *\/ 7 *Gamma(5/6)| 2/3 ____ 3 | 1 2 \1/2, 4/3 | / 2 *\/ 7 *Gamma(1/3)| \ \/ pi *Gamma(2/3) / \ \/ pi *Gamma(1/6) /
- 10*7 *\/ pi *cos (1)*|-------------------------------------- + ---------------------| - 8*7 *\/ pi *sin (1)*|----------------------------------- + ---------------------| + 8*7 *\/ pi *cos (1)*|-------------------------------------- + ---------------------| + 10*7 *\/ pi *sin (1)*|----------------------------------- + ---------------------| - ---------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------
| ____ 7*Gamma(2/3) | | ____ 7*Gamma(1/6) | | ____ 7*Gamma(2/3) | | ____ 7*Gamma(1/6) | 2 2
\ \/ pi *Gamma(1/6) / \ \/ pi *Gamma(2/3) / \ \/ pi *Gamma(1/6) / \ \/ pi *Gamma(2/3) /
$$- 10 \cdot 7^{\frac{2}{3}} \sqrt{\pi} \left(\frac{7 \Gamma\left(- \frac{5}{6}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{5}{6} \\ \frac{3}{2}, \frac{11}{6} \end{matrix}\middle| {- \frac{49}{4}} \right)}}{\sqrt{\pi} \Gamma\left(\frac{1}{6}\right)} + \frac{2^{\frac{2}{3}} \sqrt[3]{7} \Gamma\left(\frac{5}{6}\right)}{7 \Gamma\left(\frac{2}{3}\right)}\right) \cos^{3}{\left(1 \right)} + 8 \cdot 7^{\frac{2}{3}} \sqrt{\pi} \left(\frac{7 \Gamma\left(- \frac{5}{6}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{5}{6} \\ \frac{3}{2}, \frac{11}{6} \end{matrix}\middle| {- \frac{49}{4}} \right)}}{\sqrt{\pi} \Gamma\left(\frac{1}{6}\right)} + \frac{2^{\frac{2}{3}} \sqrt[3]{7} \Gamma\left(\frac{5}{6}\right)}{7 \Gamma\left(\frac{2}{3}\right)}\right) \cos^{5}{\left(1 \right)} + \frac{5 \cdot 7^{\frac{2}{3}} \sqrt{\pi} \left(\frac{7 \Gamma\left(- \frac{5}{6}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{5}{6} \\ \frac{3}{2}, \frac{11}{6} \end{matrix}\middle| {- \frac{49}{4}} \right)}}{\sqrt{\pi} \Gamma\left(\frac{1}{6}\right)} + \frac{2^{\frac{2}{3}} \sqrt[3]{7} \Gamma\left(\frac{5}{6}\right)}{7 \Gamma\left(\frac{2}{3}\right)}\right) \cos{\left(1 \right)}}{2} - 8 \cdot 7^{\frac{2}{3}} \sqrt{\pi} \left(\frac{\Gamma\left(- \frac{1}{3}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{1}{3} \\ \frac{1}{2}, \frac{4}{3} \end{matrix}\middle| {- \frac{49}{4}} \right)}}{\sqrt{\pi} \Gamma\left(\frac{2}{3}\right)} + \frac{2^{\frac{2}{3}} \sqrt[3]{7} \Gamma\left(\frac{1}{3}\right)}{7 \Gamma\left(\frac{1}{6}\right)}\right) \sin^{5}{\left(1 \right)} - \frac{5 \cdot 7^{\frac{2}{3}} \sqrt{\pi} \left(\frac{\Gamma\left(- \frac{1}{3}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{1}{3} \\ \frac{1}{2}, \frac{4}{3} \end{matrix}\middle| {- \frac{49}{4}} \right)}}{\sqrt{\pi} \Gamma\left(\frac{2}{3}\right)} + \frac{2^{\frac{2}{3}} \sqrt[3]{7} \Gamma\left(\frac{1}{3}\right)}{7 \Gamma\left(\frac{1}{6}\right)}\right) \sin{\left(1 \right)}}{2} + 10 \cdot 7^{\frac{2}{3}} \sqrt{\pi} \left(\frac{\Gamma\left(- \frac{1}{3}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{1}{3} \\ \frac{1}{2}, \frac{4}{3} \end{matrix}\middle| {- \frac{49}{4}} \right)}}{\sqrt{\pi} \Gamma\left(\frac{2}{3}\right)} + \frac{2^{\frac{2}{3}} \sqrt[3]{7} \Gamma\left(\frac{1}{3}\right)}{7 \Gamma\left(\frac{1}{6}\right)}\right) \sin^{3}{\left(1 \right)}$$
-10*7^(2/3)*sqrt(pi)*cos(1)^3*(7*gamma(-5/6)*hyper((5/6,), (3/2, 11/6), -49/4)/(sqrt(pi)*gamma(1/6)) + 2^(2/3)*7^(1/3)*gamma(5/6)/(7*gamma(2/3))) - 8*7^(2/3)*sqrt(pi)*sin(1)^5*(gamma(-1/3)*hyper((1/3,), (1/2, 4/3), -49/4)/(sqrt(pi)*gamma(2/3)) + 2^(2/3)*7^(1/3)*gamma(1/3)/(7*gamma(1/6))) + 8*7^(2/3)*sqrt(pi)*cos(1)^5*(7*gamma(-5/6)*hyper((5/6,), (3/2, 11/6), -49/4)/(sqrt(pi)*gamma(1/6)) + 2^(2/3)*7^(1/3)*gamma(5/6)/(7*gamma(2/3))) + 10*7^(2/3)*sqrt(pi)*sin(1)^3*(gamma(-1/3)*hyper((1/3,), (1/2, 4/3), -49/4)/(sqrt(pi)*gamma(2/3)) + 2^(2/3)*7^(1/3)*gamma(1/3)/(7*gamma(1/6))) - 5*7^(2/3)*sqrt(pi)*(gamma(-1/3)*hyper((1/3,), (1/2, 4/3), -49/4)/(sqrt(pi)*gamma(2/3)) + 2^(2/3)*7^(1/3)*gamma(1/3)/(7*gamma(1/6)))*sin(1)/2 + 5*7^(2/3)*sqrt(pi)*(7*gamma(-5/6)*hyper((5/6,), (3/2, 11/6), -49/4)/(sqrt(pi)*gamma(1/6)) + 2^(2/3)*7^(1/3)*gamma(5/6)/(7*gamma(2/3)))*cos(1)/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.