What is the integral of 7x^2+3+6/(x^2+1) ?

The integral of 7x^2+3+6/(x^2+1) is (7x^3)/3+3x+6arctan(x)+C

Popular >

integral of 7x^2+3+6/(x^2+1)

\int 7 x^{2} + 3 + \frac{6}{x ^{2} + 1} d x

\frac{7 x ^{3}}{3} + 3 x + 6 arctan (x) + C

Solution steps

\int 7 x^{2} + 3 + \frac{6}{x ^{2} + 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

= \int 7 x^{2} d x + \int 3 d x + \int \frac{6}{x ^{2} + 1} d x

\int 7 x^{2} d x = \frac{7 x ^{3}}{3}

\int 3 d x = 3 x

\int \frac{6}{x ^{2} + 1} d x = 6 arctan (x)

= \frac{7 x ^{3}}{3} + 3 x + 6 arctan (x)

Add a constant to the solution

= \frac{7 x ^{3}}{3} + 3 x + 6 arctan (x) + C

\frac{d}{d x} (\frac{16}{( 5 - x ) ^{2}} - 1)

(\frac{π}{2})^{^{'}}

\int_{0}^{4} 16 - x^{2} d x

3 x^{e} + 2 e^{x}

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

What is the integral of 7x^2+3+6/(x^2+1) ?
The integral of 7x^2+3+6/(x^2+1) is (7x^3)/3+3x+6arctan(x)+C