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

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

Popular >

integral of (4x^2)/(x^2+1)

\int \frac{4 x ^{2}}{x ^{2} + 1} d x

4 (- arctan (x) + x) + C

Solution steps

\int \frac{4 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

= 4 \cdot \int \frac{x ^{2}}{x ^{2} + 1} d x

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

= 4 \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

= 4 (- \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

= 4 (- arctan (x) + x)

Add a constant to the solution

= 4 (- arctan (x) + x) + C

\int x (8 x)^{\frac{3}{2}} + 7 d x

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

\int 7 x - x^{2} d x

\int - \frac{200 x}{( 14 + \frac{1}{2} x ^{2} ) ^{\frac{3}{2}}} d x

\int \frac{x ^{4} + 1}{x ^{5} + 5 x} d x

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