Sr Examen
Integral de (x-(x-(sqrt(2)+1)*log(tan(x/2+pi/4))-(sqrt(2)+1)*x))^2 dx
Solución
Ha introducido
[src]
pi -- 4 / | | 2 | / / ___ \ / /x pi\\ / ___ \ \ | |x + -x + \\/ 2 + 1/*log|tan|- + --|| + \\/ 2 + 1/*x| dx | \ \ \2 4 // / | / 0
$$\int\limits_{0}^{\frac{\pi}{4}} \left(x + \left(x \left(1 + \sqrt{2}\right) + \left(- x + \left(1 + \sqrt{2}\right) \log{\left(\tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)} \right)}\right)\right)\right)^{2}\, dx$$
Integral((x - x + (sqrt(2) + 1)*log(tan(x/2 + pi/4)) + (sqrt(2) + 1)*x)^2, (x, 0, pi/4))
Respuesta (Indefinida)
[src]
/ / / \
| | | |
| 2 | | 2 |
| x / | | x / |
3* | ----------- dx | | | ----------- dx | |
| /x pi\ | 2 /x pi\ | | /x pi\ | 2 /x pi\ |
/ | tan|- + --| 3* | x *tan|- + --| dx | | tan|- + --| | x *tan|- + --| dx |
| / | \2 4 / | \2 4 / / | | \2 4 / | \2 4 / 2 / /x pi\\|
| 2 | | | | | | | x *log|tan|- + --||| ___ 3
| / / ___ \ / /x pi\\ / ___ \ \ 3 | 2/ /x pi\\ / / ___ | 2/ /x pi\\ 2 / /x pi\\ ___ | / / \ \2 4 //| 2*\/ 2 *x
| |x + -x + \\/ 2 + 1/*log|tan|- + --|| + \\/ 2 + 1/*x| dx = C + x + 3* | log |tan|- + --|| dx - ------------------- - ---------------------- + 2*\/ 2 * | log |tan|- + --|| dx + 3*x *log|tan|- + --|| + 4*\/ 2 *|- ----------------- - -------------------- + -------------------| + ----------
| \ \ \2 4 // / | \ \2 4 // 2 2 | \ \2 4 // \ \2 4 // \ 4 4 2 / 3
| | |
/ / /
$$\int \left(x + \left(x \left(1 + \sqrt{2}\right) + \left(- x + \left(1 + \sqrt{2}\right) \log{\left(\tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)} \right)}\right)\right)\right)^{2}\, dx = C + \frac{2 \sqrt{2} x^{3}}{3} + x^{3} + 3 x^{2} \log{\left(\tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)} \right)} + 4 \sqrt{2} \left(\frac{x^{2} \log{\left(\tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)} \right)}}{2} - \frac{\int \frac{x^{2}}{\tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)}}\, dx}{4} - \frac{\int x^{2} \tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)}\, dx}{4}\right) - \frac{3 \int \frac{x^{2}}{\tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)}}\, dx}{2} - \frac{3 \int x^{2} \tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)}\, dx}{2} + 2 \sqrt{2} \int \log{\left(\tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)} \right)}^{2}\, dx + 3 \int \log{\left(\tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)} \right)}^{2}\, dx$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.