Sr Examen
Integral de ((arctg2x)^1/5)/1+4x^2 dx
Solución
Ha introducido
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1 / | | /5 ___________ \ | |\/ atan(2*x) 2| | |------------- + 4*x | dx | \ 1 / | / 0
$$\int\limits_{0}^{1} \left(4 x^{2} + \frac{\sqrt[5]{\operatorname{atan}{\left(2 x \right)}}}{1}\right)\, dx$$
Integral(atan(2*x)^(1/5)/1 + 4*x^2, (x, 0, 1))
Respuesta (Indefinida)
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/ | / | /5 ___________ \ 3 | | |\/ atan(2*x) 2| 4*x | 5 ___________ | |------------- + 4*x | dx = C + ---- + | \/ atan(2*x) dx | \ 1 / 3 | | / /
$$\int \left(4 x^{2} + \frac{\sqrt[5]{\operatorname{atan}{\left(2 x \right)}}}{1}\right)\, dx = C + \frac{4 x^{3}}{3} + \int \sqrt[5]{\operatorname{atan}{\left(2 x \right)}}\, dx$$
Respuesta
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1 / | | /5 ___________ 2\ | \\/ atan(2*x) + 4*x / dx | / 0
$$\int\limits_{0}^{1} \left(4 x^{2} + \sqrt[5]{\operatorname{atan}{\left(2 x \right)}}\right)\, dx$$
=
=
1 / | | /5 ___________ 2\ | \\/ atan(2*x) + 4*x / dx | / 0
$$\int\limits_{0}^{1} \left(4 x^{2} + \sqrt[5]{\operatorname{atan}{\left(2 x \right)}}\right)\, dx$$
Integral(atan(2*x)^(1/5) + 4*x^2, (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.