What is the integral of (1+5x^4)arctan(x^2) ?

The integral of (1+5x^4)arctan(x^2) is arctan(x^2)(x+x^5)-(2x^3)/3+C

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integral of (1+5x^4)arctan(x^2)

\int (1 + 5 x^{4}) arctan (x^{2}) d x

arctan (x^{2}) (x + x^{5}) - \frac{2 x ^{3}}{3} + C

Solution steps

\int (1 + 5 x^{4}) arctan (x^{2}) d x

Apply Integration By Parts

: arctan (x^{2}) (x + x^{5}) - \int 2 x^{2} d x

= arctan (x^{2}) (x + x^{5}) - \int 2 x^{2} d x

\int 2 x^{2} d x = \frac{2 x ^{3}}{3}

= arctan (x^{2}) (x + x^{5}) - \frac{2 x ^{3}}{3}

Add a constant to the solution

= arctan (x^{2}) (x + x^{5}) - \frac{2 x ^{3}}{3} + C

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What is the integral of (1+5x^4)arctan(x^2) ?
The integral of (1+5x^4)arctan(x^2) is arctan(x^2)(x+x^5)-(2x^3)/3+C