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

The integral of (2x+1)/(sqrt(9-x^2)) is -2sqrt(9-x^2)+arcsin(1/3 x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x+1)/(sqrt(9-x^2))

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

- 2 9 - x^{2} + arcsin (\frac{1}{3} x) + C

Solution steps

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

Expand

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

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

\int \frac{2 x}{9 - x ^{2}} d x = - 2 9 - x^{2}

\int \frac{1}{9 - x ^{2}} d x = arcsin (\frac{1}{3} x)

= - 2 9 - x^{2} + arcsin (\frac{1}{3} x)

Add a constant to the solution

= - 2 9 - x^{2} + arcsin (\frac{1}{3} x) + C

\int \frac{5}{2} x^{2} d x

\int \frac{x}{3 x ^{2} + 7} d x

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

\int e^{4 x} 4 d x

\int (3 x^{4} - 5 x + 1) d x

What is the integral of (2x+1)/(sqrt(9-x^2)) ?
The integral of (2x+1)/(sqrt(9-x^2)) is -2sqrt(9-x^2)+arcsin(1/3 x)+C