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