What is the integral of (9+8x)/(1+x^2) ?

The integral of (9+8x)/(1+x^2) is 9arctan(x)+4ln|1+x^2|+C

Popular >

integral of (9+8x)/(1+x^2)

\int \frac{9 + 8 x}{1 + x ^{2}} d x

9 arctan (x) + 4 ln 1 + x^{2} + C

Solution steps

\int \frac{9 + 8 x}{1 + x ^{2}} d x

Expand

\frac{9 + 8 x}{1 + x ^{2}} : \frac{9}{1 + x ^{2}} + \frac{8 x}{1 + x ^{2}}

Apply the Sum Rule:

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

= \int \frac{9}{1 + x ^{2}} d x + \int \frac{8 x}{1 + x ^{2}} d x

\int \frac{9}{1 + x ^{2}} d x = 9 arctan (x)

\int \frac{8 x}{1 + x ^{2}} d x = 4 ln 1 + x^{2}

= 9 arctan (x) + 4 ln 1 + x^{2}

Add a constant to the solution

= 9 arctan (x) + 4 ln 1 + x^{2} + C

\int sec (2) (x) (1 + tan (x)) d x

\int 6 x e^{4 x} d x

\int \frac{( m - 15 ) x - ( m + 20 )}{3 x ^{2} + x - 4} d x

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

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

What is the integral of (9+8x)/(1+x^2) ?
The integral of (9+8x)/(1+x^2) is 9arctan(x)+4ln|1+x^2|+C