Sr Examen
Integral de x^(1/4)/(1+x)^2 dx
Solución
Ha introducido
[src]
oo / | | 4 ___ | \/ x | -------- dx | 2 | (1 + x) | / 0
$$\int\limits_{0}^{\infty} \frac{\sqrt[4]{x}}{\left(x + 1\right)^{2}}\, dx$$
Integral(x^(1/4)/(1 + x)^2, (x, 0, oo))
Respuesta (Indefinida)
[src]
/ | | 4 ___ 4 ___ ___ / ___ ___ 4 ___\ ___ / ___ ___ 4 ___\ ___ / ___ 4 ___\ ___ / ___ 4 ___\ ___ / ___ ___ 4 ___\ ___ / ___ ___ 4 ___\ ___ / ___ 4 ___\ ___ / ___ 4 ___\ | \/ x 8*\/ x \/ 2 *log\4 + 4*\/ x + 4*\/ 2 *\/ x / \/ 2 *log\4 + 4*\/ x - 4*\/ 2 *\/ x / 2*\/ 2 *atan\1 + \/ 2 *\/ x / 2*\/ 2 *atan\-1 + \/ 2 *\/ x / x*\/ 2 *log\4 + 4*\/ x + 4*\/ 2 *\/ x / x*\/ 2 *log\4 + 4*\/ x - 4*\/ 2 *\/ x / 2*x*\/ 2 *atan\1 + \/ 2 *\/ x / 2*x*\/ 2 *atan\-1 + \/ 2 *\/ x / | -------- dx = C - ------- + -------------------------------------- - -------------------------------------- + ----------------------------- + ------------------------------ + ---------------------------------------- - ---------------------------------------- + ------------------------------- + -------------------------------- | 2 8 + 8*x 8 + 8*x 8 + 8*x 8 + 8*x 8 + 8*x 8 + 8*x 8 + 8*x 8 + 8*x 8 + 8*x | (1 + x) | /
$$\int \frac{\sqrt[4]{x}}{\left(x + 1\right)^{2}}\, dx = C - \frac{8 \sqrt[4]{x}}{8 x + 8} - \frac{\sqrt{2} x \log{\left(- 4 \sqrt{2} \sqrt[4]{x} + 4 \sqrt{x} + 4 \right)}}{8 x + 8} + \frac{\sqrt{2} x \log{\left(4 \sqrt{2} \sqrt[4]{x} + 4 \sqrt{x} + 4 \right)}}{8 x + 8} + \frac{2 \sqrt{2} x \operatorname{atan}{\left(\sqrt{2} \sqrt[4]{x} - 1 \right)}}{8 x + 8} + \frac{2 \sqrt{2} x \operatorname{atan}{\left(\sqrt{2} \sqrt[4]{x} + 1 \right)}}{8 x + 8} - \frac{\sqrt{2} \log{\left(- 4 \sqrt{2} \sqrt[4]{x} + 4 \sqrt{x} + 4 \right)}}{8 x + 8} + \frac{\sqrt{2} \log{\left(4 \sqrt{2} \sqrt[4]{x} + 4 \sqrt{x} + 4 \right)}}{8 x + 8} + \frac{2 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt[4]{x} - 1 \right)}}{8 x + 8} + \frac{2 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt[4]{x} + 1 \right)}}{8 x + 8}$$
Respuesta
[src]
___ pi*\/ 2 -------- 4
$$\frac{\sqrt{2} \pi}{4}$$
=
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___ pi*\/ 2 -------- 4
$$\frac{\sqrt{2} \pi}{4}$$
pi*sqrt(2)/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.