What is the integral of 1/(sqrt(64-x^2)) ?

The integral of 1/(sqrt(64-x^2)) is arcsin(1/8 x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 1/(sqrt(64-x^2))

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

arcsin (\frac{1}{8} x) + C

Solution steps

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

Apply Trigonometric Substitution

= \int 1 d u

Integral of a constant:

\int a d x = a x

= 1 \cdot u

Substitute back

u = arcsin (\frac{1}{8} x)

= 1 \cdot arcsin (\frac{1}{8} x)

Simplify

= arcsin (\frac{1}{8} x)

Add a constant to the solution

= arcsin (\frac{1}{8} x) + C

What is the integral of 1/(sqrt(64-x^2)) ?
The integral of 1/(sqrt(64-x^2)) is arcsin(1/8 x)+C