What is the integral of (x^2+58)/(x^2+64) ?

The integral of (x^2+58)/(x^2+64) is -3/4 arctan(x/8)+x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x^2+58)/(x^2+64)

\int \frac{x ^{2} + 58}{x ^{2} + 64} d x

- \frac{3}{4} arctan (\frac{x}{8}) + x + C

Solution steps

\int \frac{x ^{2} + 58}{x ^{2} + 64} d x

\frac{x ^{2} + 58}{x ^{2} + 64} = - \frac{6}{x ^{2} + 64} + 1

= \int - \frac{6}{x ^{2} + 64} + 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{6}{x ^{2} + 64} d x + \int 1 d x

\int \frac{6}{x ^{2} + 64} d x = \frac{3}{4} arctan (\frac{x}{8})

\int 1 d x = x

= - \frac{3}{4} arctan (\frac{x}{8}) + x

Add a constant to the solution

= - \frac{3}{4} arctan (\frac{x}{8}) + x + C

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

\int (x^{3} + 2)^{5} d x

\int - 4 x^{- 2} d x

\int x^{m} ln (x) d x

What is the integral of (x^2+58)/(x^2+64) ?
The integral of (x^2+58)/(x^2+64) is -3/4 arctan(x/8)+x+C