Sr Examen
Integral de (x^2+2x+1)arctan(x+1) dx
Solución
Ha introducido
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1 / | | / 2 \ | \x + 2*x + 1/*atan(x + 1) dx | / 0
$$\int\limits_{0}^{1} \left(\left(x^{2} + 2 x\right) + 1\right) \operatorname{atan}{\left(x + 1 \right)}\, dx$$
Integral((x^2 + 2*x + 1)*atan(x + 1), (x, 0, 1))
Respuesta (Indefinida)
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/ | / 2\ 2 / 2 \ 3 | / 2 \ 2*atan(1 + x) log\1 + (1 + x) / x x 2*log\2 + x + 2*x/ 2 x *atan(1 + x) | \x + 2*x + 1/*atan(x + 1) dx = C - ------------- - ----------------- - - - -- + ------------------- + x *atan(1 + x) + (1 + x)*atan(1 + x) + -------------- | 3 2 3 6 3 3 /
$$\int \left(\left(x^{2} + 2 x\right) + 1\right) \operatorname{atan}{\left(x + 1 \right)}\, dx = C + \frac{x^{3} \operatorname{atan}{\left(x + 1 \right)}}{3} + x^{2} \operatorname{atan}{\left(x + 1 \right)} - \frac{x^{2}}{6} - \frac{x}{3} + \left(x + 1\right) \operatorname{atan}{\left(x + 1 \right)} - \frac{\log{\left(\left(x + 1\right)^{2} + 1 \right)}}{2} + \frac{2 \log{\left(x^{2} + 2 x + 2 \right)}}{3} - \frac{2 \operatorname{atan}{\left(x + 1 \right)}}{3}$$
Gráfica
Respuesta
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1 log(2) pi log(5) 8*atan(2) - - - ------ - -- + ------ + --------- 2 6 12 6 3
$$- \frac{1}{2} - \frac{\pi}{12} - \frac{\log{\left(2 \right)}}{6} + \frac{\log{\left(5 \right)}}{6} + \frac{8 \operatorname{atan}{\left(2 \right)}}{3}$$
=
=
1 log(2) pi log(5) 8*atan(2) - - - ------ - -- + ------ + --------- 2 6 12 6 3
$$- \frac{1}{2} - \frac{\pi}{12} - \frac{\log{\left(2 \right)}}{6} + \frac{\log{\left(5 \right)}}{6} + \frac{8 \operatorname{atan}{\left(2 \right)}}{3}$$
-1/2 - log(2)/6 - pi/12 + log(5)/6 + 8*atan(2)/3
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.