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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/((sqrt(a^2-x^2)))

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

arcsin (\frac{x}{a}) + C

Solution steps

\int \frac{1}{a ^{2} - x ^{2}} d x

Apply Trigonometric Substitution

: \int 1 d u

= \int 1 d u

Integral of a constant:

\int a d x = a x

= 1 \cdot u

Substitute back

u = arcsin (\frac{1}{a} x)

= 1 \cdot arcsin (\frac{1}{a} x)

Simplify

1 \cdot arcsin (\frac{1}{a} x) : arcsin (\frac{x}{a})

= arcsin (\frac{x}{a})

Add a constant to the solution

= arcsin (\frac{x}{a}) + C

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

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

\int \frac{4 x}{2 x ^{2} + 5} d x

\int 7 tan (3 x) ln (cos (3 x)) d x

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

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