What is the integral of 1/(sqrt((a^2+x^2)^3)) ?

The integral of 1/(sqrt((a^2+x^2)^3)) is x/(a^2sqrt(a^2+x^2))+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((a^2+x^2)^3))

\int \frac{1}{( a ^{2} + x ^{2} ) ^{3}} d x

\frac{x}{a ^{2} a ^{2} + x ^{2}} + C

Solution steps

\int \frac{1}{( a ^{2} + x ^{2} ) ^{3}} d x

Apply Integral Substitution

= \int \frac{1}{a ^{2} ( u ^{2} + 1 ) ^{\frac{3}{2}}} d u

Take the constant out:

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

= \frac{1}{a ^{2}} \cdot \int \frac{1}{( u ^{2} + 1 ) ^{\frac{3}{2}}} d u

Apply Trigonometric Substitution

: \int cos (v) d v

= \frac{1}{a ^{2}} \cdot \int cos (v) d v

Use the common integral:

\int cos (v) d v = sin (v)

= \frac{1}{a ^{2}} sin (v)

Substitute back

= \frac{1}{a ^{2}} sin (arctan (\frac{x}{a}))

Simplify

\frac{1}{a ^{2}} sin (arctan (\frac{x}{a})) : \frac{x}{a ^{2} a ^{2} + x ^{2}}

= \frac{x}{a ^{2} a ^{2} + x ^{2}}

Add a constant to the solution

= \frac{x}{a ^{2} a ^{2} + x ^{2}} + C

\int - 0.015 e^{- 0.01 x} d x

\int e^{9 x + 2} d x

\int (y - e^{x} z^{2}) d x

\int e^{x} + \frac{1}{3 x} d x

\int p (p + 4)^{6} d p

What is the integral of 1/(sqrt((a^2+x^2)^3)) ?
The integral of 1/(sqrt((a^2+x^2)^3)) is x/(a^2sqrt(a^2+x^2))+C