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

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

Popular >

integral of 1/(sqrt(1-ax^2))

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

\frac{1}{a} arcsin (a x) + C

Solution steps

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

Apply Trigonometric Substitution

: \int \frac{1}{a} d u

= \int \frac{1}{a} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{a} \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= \frac{1}{a} \cdot 1 \cdot u

Substitute back

u = arcsin (a x)

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

Simplify

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

Add a constant to the solution

= \frac{1}{a} arcsin (a x) + C

\int \frac{3 x ^{3} - 9 x ^{2} + 9 x + 3}{3 x - 3} d x

\int x ln (9 x) d x

\int sin^{3} (7 θ) cos (7 θ) d θ

\int \frac{( x ^{4} )}{1 - x ^{10}} d x

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

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