What is the integral of 1/(1+x^2)+(12)/(sqrt(1-x^2)) ?

The integral of 1/(1+x^2)+(12)/(sqrt(1-x^2)) is arctan(x)+12arcsin(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(1+x^2)+(12)/(sqrt(1-x^2))

\int \frac{1}{1 + x ^{2}} + \frac{12}{1 - x ^{2}} d x

arctan (x) + 12 arcsin (x) + C

Solution steps

\int \frac{1}{1 + x ^{2}} + \frac{12}{1 - x ^{2}} 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{1}{1 + x ^{2}} d x + \int \frac{12}{1 - x ^{2}} d x

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

\int \frac{12}{1 - x ^{2}} d x = 12 arcsin (x)

= arctan (x) + 12 arcsin (x)

Add a constant to the solution

= arctan (x) + 12 arcsin (x) + C

\int \frac{6 x + 8}{( x + 3 ) ( x + 5 ) ( x - 2 )} d x

\int (5 - e^{2 x})^{2} d x

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

\int 15 x ln (1 + x) d x

\int tan^{5} (2 x) sec^{8} (2 x) d x

What is the integral of 1/(1+x^2)+(12)/(sqrt(1-x^2)) ?
The integral of 1/(1+x^2)+(12)/(sqrt(1-x^2)) is arctan(x)+12arcsin(x)+C