What is the integral of (2x^2)/((x^2+1)) ?

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

Popular >

integral of (2x^2)/((x^2+1))

integral

\frac{2 x ^{2}}{( x ^{2} + 1 )}

2 (- arctan (x) + x) + C

Solution steps

\int \frac{2 x ^{2}}{x ^{2} + 1} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int \frac{x ^{2}}{x ^{2} + 1} d x

\frac{x ^{2}}{x ^{2} + 1} = - \frac{1}{x ^{2} + 1} + 1

= 2 \cdot \int - \frac{1}{x ^{2} + 1} + 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

\int 1 d x = x

= 2 (- arctan (x) + x)

Add a constant to the solution

= 2 (- arctan (x) + x) + C

2 - x^{2}

\frac{( 6 x + 1 )}{( 2 x - 3 )}

\frac{9}{( 3 x - 4 ) ^{2}}

x^{5} cos (3 x)

y^{4} (1 - y)^{3}

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