What is the integral of ((x^2+13))/((x^2+16)) ?

The integral of ((x^2+13))/((x^2+16)) is -3/4 arctan(x/4)+x+C

Popular >

integral of ((x^2+13))/((x^2+16))

\int \frac{( x ^{2} + 13 )}{( x ^{2} + 16 )} d x

- \frac{3}{4} arctan (\frac{x}{4}) + x + C

Solution steps

\int \frac{x ^{2} + 13}{x ^{2} + 16} d x

\frac{x ^{2} + 13}{x ^{2} + 16} = - \frac{3}{x ^{2} + 16} + 1

= \int - \frac{3}{x ^{2} + 16} + 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 \frac{3}{x ^{2} + 16} d x + \int 1 d x

\int \frac{3}{x ^{2} + 16} d x = \frac{3}{4} arctan (\frac{x}{4})

\int 1 d x = x

= - \frac{3}{4} arctan (\frac{x}{4}) + x

Add a constant to the solution

= - \frac{3}{4} arctan (\frac{x}{4}) + x + C

\int (x^{3} + 6 x + 1) d x

\int 8 tan (4 x) d x

\int \frac{3}{sin ( x )} d x

\int \frac{x}{9 x ^{2} + 4} d x

\int \frac{- 6 x ^{2} + 3 x + 5}{x ^{3} - x} d x

What is the integral of ((x^2+13))/((x^2+16)) ?
The integral of ((x^2+13))/((x^2+16)) is -3/4 arctan(x/4)+x+C