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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

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

Solution steps

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

Apply Trigonometric Substitution

= \int 1 d v

Integral of a constant:

\int a d x = a x

= 1 \cdot v

Substitute back

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

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

Simplify

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

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

Add a constant to the solution

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

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