What is the integral of xarctan(x^2) ?

The integral of xarctan(x^2) is 1/2 x^2arctan(x^2)-1/4 ln|x^4+1|+C

Popular >

integral of xarctan(x^2)

\int x arctan (x^{2}) d x

\frac{1}{2} x^{2} arctan (x^{2}) - \frac{1}{4} ln x^{4} + 1 + C

Solution steps

\int x arctan (x^{2}) d x

Apply Integration By Parts

: \frac{1}{2} x^{2} arctan (x^{2}) - \int \frac{x ^{3}}{x ^{4} + 1} d x

= \frac{1}{2} x^{2} arctan (x^{2}) - \int \frac{x ^{3}}{x ^{4} + 1} d x

\int \frac{x ^{3}}{x ^{4} + 1} d x = \frac{1}{4} ln x^{4} + 1

= \frac{1}{2} x^{2} arctan (x^{2}) - \frac{1}{4} ln x^{4} + 1

Add a constant to the solution

= \frac{1}{2} x^{2} arctan (x^{2}) - \frac{1}{4} ln x^{4} + 1 + C

\frac{2 t ^{2} + 1}{t}

\frac{d}{d x} (x e^{- x})

f (x) = cos (4 x)

f (x) = 2 x, at x = 4

y^{^{'}} = \frac{3 x ^{2} + 2 x - 4}{2 y - 4}, y (2) = 0

What is the integral of xarctan(x^2) ?
The integral of xarctan(x^2) is 1/2 x^2arctan(x^2)-1/4 ln|x^4+1|+C