What is the integral of (21)/((1-x^2)^{3/2)} ?

The integral of (21)/((1-x^2)^{3/2)} is (21x)/((1-x^2)^{1/2)}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (21)/((1-x^2)^{3/2)}

\int \frac{21}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

\frac{21 x}{( 1 - x ^{2} ) ^{\frac{1}{2}}} + C

Solution steps

\int \frac{21}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

Take the constant out:

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

= 21 \cdot \int \frac{1}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

Apply Trigonometric Substitution

: \int sec^{2} (u) d u

= 21 \cdot \int sec^{2} (u) d u

Use the common integral:

\int sec^{2} (u) d u = tan (u)

= 21 tan (u)

Substitute back

u = arcsin (x)

= 21 tan (arcsin (x))

Simplify

21 tan (arcsin (x)) : \frac{21 x}{( 1 - x ^{2} ) ^{\frac{1}{2}}}

= \frac{21 x}{( 1 - x ^{2} ) ^{\frac{1}{2}}}

Add a constant to the solution

= \frac{21 x}{( 1 - x ^{2} ) ^{\frac{1}{2}}} + C

(- 10 - 6) (- 10 - 5)

\frac{d y}{d t} = sin (y)

\int \frac{p}{p ^{2} + 1} d p

\int \frac{arcsin ( x )}{x ^{2}} d x

\frac{\partial}{\partial x} (x + 2)

What is the integral of (21)/((1-x^2)^{3/2)} ?
The integral of (21)/((1-x^2)^{3/2)} is (21x)/((1-x^2)^{1/2)}+C