What is the integral of 1/(sqrt(25-36x^2)) ?

The integral of 1/(sqrt(25-36x^2)) is 1/6 arcsin(6/5 x)+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(25-36x^2))

\int \frac{1}{25 - 36 x ^{2}} d x

\frac{1}{6} arcsin (\frac{6}{5} x) + C

Solution steps

\int \frac{1}{25 - 36 x ^{2}} d x

Apply Trigonometric Substitution

: \int \frac{1}{6} d u

= \int \frac{1}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= \frac{1}{6} \cdot 1 \cdot u

Substitute back

u = arcsin (\frac{6}{5} x)

= \frac{1}{6} \cdot 1 \cdot arcsin (\frac{6}{5} x)

Simplify

= \frac{1}{6} arcsin (\frac{6}{5} x)

Add a constant to the solution

= \frac{1}{6} arcsin (\frac{6}{5} x) + C

\int 13 tan^{2} (x) sec^{3} (x) d x

\int - 2 x^{2} + 8 x d x

y^{^{''}} - 3 y^{^{'}} + y = 0

y = 3 x^{3} - 3 x

\frac{d y}{d x} = 5 e^{x}

What is the integral of 1/(sqrt(25-36x^2)) ?
The integral of 1/(sqrt(25-36x^2)) is 1/6 arcsin(6/5 x)+C