What is the integral of (x^2+44)/(x^2+49) ?

The integral of (x^2+44)/(x^2+49) is -5/7 arctan(x/7)+x+C

Popular >

integral of (x^2+44)/(x^2+49)

\int \frac{x ^{2} + 44}{x ^{2} + 49} d x

- \frac{5}{7} arctan (\frac{x}{7}) + x + C

Solution steps

\int \frac{x ^{2} + 44}{x ^{2} + 49} d x

\frac{x ^{2} + 44}{x ^{2} + 49} = - \frac{5}{x ^{2} + 49} + 1

= \int - \frac{5}{x ^{2} + 49} + 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{5}{x ^{2} + 49} d x + \int 1 d x

\int \frac{5}{x ^{2} + 49} d x = \frac{5}{7} arctan (\frac{x}{7})

\int 1 d x = x

= - \frac{5}{7} arctan (\frac{x}{7}) + x

Add a constant to the solution

= - \frac{5}{7} arctan (\frac{x}{7}) + x + C

\int e^{a y} cos (b y) d y

\int sin (x) (2 x) d x

\int 6 x^{2} - 6 x - 36 d x

\int \frac{3 x - 1}{x ^{2} + 4 x + 13} d x

\int (sin (x) + e^{x})^{2} d x

What is the integral of (x^2+44)/(x^2+49) ?
The integral of (x^2+44)/(x^2+49) is -5/7 arctan(x/7)+x+C