Sr Examen
Integral de cos5(x^2) dx
Solución
Ha introducido
[src]
1/10 / | | 5/ 2\ | cos \x / dx | / 0
$$\int\limits_{0}^{\frac{1}{10}} \cos^{5}{\left(x^{2} \right)}\, dx$$
Integral(cos(x^2)^5, (x, 0, 1/10))
Respuesta (Indefinida)
[src]
/ ____\ / ___\ / ___\
____ ____ |x*\/ 10 | ___ ____ |x*\/ 2 | ___ ____ |x*\/ 6 |
/ \/ 10 *\/ pi *C|--------|*Gamma(1/4) 5*\/ 2 *\/ pi *C|-------|*Gamma(1/4) 5*\/ 6 *\/ pi *C|-------|*Gamma(1/4)
| | ____ | | ____| | ____|
| 5/ 2\ \ \/ pi / \ \/ pi / \ \/ pi /
| cos \x / dx = C + ------------------------------------ + ------------------------------------ + ------------------------------------
| 640*Gamma(5/4) 64*Gamma(5/4) 384*Gamma(5/4)
/
$$\int \cos^{5}{\left(x^{2} \right)}\, dx = C + \frac{\sqrt{10} \sqrt{\pi} C\left(\frac{\sqrt{10} x}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{640 \Gamma\left(\frac{5}{4}\right)} + \frac{5 \sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{64 \Gamma\left(\frac{5}{4}\right)} + \frac{5 \sqrt{6} \sqrt{\pi} C\left(\frac{\sqrt{6} x}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{384 \Gamma\left(\frac{5}{4}\right)}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.