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

The integral of x^2arctan(5x) is 1/3 x^3arctan(5x)-1/750 (25x^2+1-ln|25x^2+1|)+C

integral of x^2arctan(5x)

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

\frac{1}{3} x^{3} arctan (5 x) - \frac{1}{750} (25 x^{2} + 1 - ln 25 x^{2} + 1) + C

Solution steps

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

Apply Integration By Parts

= \frac{1}{3} x^{3} arctan (5 x) - \int \frac{5 x ^{3}}{3 ( 25 x ^{2} + 1 )} d x

\int \frac{5 x ^{3}}{3 ( 25 x ^{2} + 1 )} d x = \frac{1}{750} (25 x^{2} + 1 - ln 25 x^{2} + 1)

= \frac{1}{3} x^{3} arctan (5 x) - \frac{1}{750} (25 x^{2} + 1 - ln 25 x^{2} + 1)

Add a constant to the solution

= \frac{1}{3} x^{3} arctan (5 x) - \frac{1}{750} (25 x^{2} + 1 - ln 25 x^{2} + 1) + C

\int 4^{- 2 x} d x

d er i v a t i v e (4 x + 1)^{2}

t an g e n t f (x) = (x^{3} - 25 x)^{14}, (5, 0)

x \to 2 lim (12 x^{2})

\int \frac{sech ( \frac{1}{x} ) tanh ( \frac{1}{x} )}{x ^{2}} d x

What is the integral of x^2arctan(5x) ?
The integral of x^2arctan(5x) is 1/3 x^3arctan(5x)-1/750 (25x^2+1-ln|25x^2+1|)+C