Sr Examen
Integral de (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 + - \\/ 2 + 1/*log|tan|- + --|| + \\/ 2 + 1/*x| dx | \ \ \2 4 // / | / 0
$$\int\limits_{0}^{\frac{\pi}{4}} \left(x + \left(x \left(1 + \sqrt{2}\right) - \left(1 + \sqrt{2}\right) \log{\left(\tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)} \right)}\right)\right)^{2}\, dx$$
Integral((x - (sqrt(2) + 1)*log(tan(x/2 + pi/4)) + (sqrt(2) + 1)*x)^2, (x, 0, pi/4))
Respuesta (Indefinida)
[src]
/ / \
| | |
| | 2 |
| | x / |
| | ----------- dx | |
| | /x pi\ | 2 /x pi\ |
/ / | | tan|- + --| | x *tan|- + --| dx |
| | / / | | \2 4 / | \2 4 / 2 / /x pi\\| /
| 2 | 2 | | | | | x *log|tan|- + --||| | ___ 3
| / / ___ \ / /x pi\\ / ___ \ \ 3 | x | 2 /x pi\ | 2/ /x pi\\ ___ | / / \ \2 4 //| 2 / /x pi\\ ___ | 2/ /x pi\\ 4*\/ 2 *x
| |x + - \\/ 2 + 1/*log|tan|- + --|| + \\/ 2 + 1/*x| dx = C + 2*x + 2* | ----------- dx + 2* | x *tan|- + --| dx + 3* | log |tan|- + --|| dx - 6*\/ 2 *|- ----------------- - -------------------- + -------------------| - 4*x *log|tan|- + --|| + 2*\/ 2 * | log |tan|- + --|| dx + ----------
| \ \ \2 4 // / | /x pi\ | \2 4 / | \ \2 4 // \ 4 4 2 / \ \2 4 // | \ \2 4 // 3
| | tan|- + --| | | |
/ | \2 4 / / / /
|
/
$$\int \left(x + \left(x \left(1 + \sqrt{2}\right) - \left(1 + \sqrt{2}\right) \log{\left(\tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)} \right)}\right)\right)^{2}\, dx = C + \frac{4 \sqrt{2} x^{3}}{3} + 2 x^{3} - 4 x^{2} \log{\left(\tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)} \right)} - 6 \sqrt{2} \left(\frac{x^{2} \log{\left(\tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)} \right)}}{2} - \frac{\int \frac{x^{2}}{\tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)}}\, dx}{4} - \frac{\int x^{2} \tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)}\, dx}{4}\right) + 2 \int \frac{x^{2}}{\tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)}}\, dx + 2 \int x^{2} \tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)}\, dx + 2 \sqrt{2} \int \log{\left(\tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)} \right)}^{2}\, dx + 3 \int \log{\left(\tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)} \right)}^{2}\, dx$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.