What is the integral of x/((49-x^2)^{3/2)} ?

The integral of x/((49-x^2)^{3/2)} is 1/((49-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 x/((49-x^2)^{3/2)}

\int \frac{x}{( 49 - x ^{2} ) ^{\frac{3}{2}}} d x

\frac{1}{( 49 - x ^{2} ) ^{\frac{1}{2}}} + C

Solution steps

\int \frac{x}{( 49 - x ^{2} ) ^{\frac{3}{2}}} d x

Apply u-substitution

: \int - \frac{1}{2 u ^{\frac{3}{2}}} d u

= \int - \frac{1}{2 u ^{\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}{2} \cdot \int \frac{1}{u ^{\frac{3}{2}}} d u

Apply the Power Rule

: - \frac{2}{u ^{\frac{1}{2}}}

= - \frac{1}{2} (- \frac{2}{u ^{\frac{1}{2}}})

Substitute back

u = 49 - x^{2}

= - \frac{1}{2} (- \frac{2}{( 49 - x ^{2} ) ^{\frac{1}{2}}})

Simplify

- \frac{1}{2} (- \frac{2}{( 49 - x ^{2} ) ^{\frac{1}{2}}}) : \frac{1}{( 49 - x ^{2} ) ^{\frac{1}{2}}}

= \frac{1}{( 49 - x ^{2} ) ^{\frac{1}{2}}}

Add a constant to the solution

= \frac{1}{( 49 - x ^{2} ) ^{\frac{1}{2}}} + C

\int \frac{x ^{6} + 30 x ^{5} - 25 x ^{4}}{5 x} d x

\int \frac{2}{x ^{2} + 2 x + 10} d x

\int \frac{x ^{7}}{( 3 - x ^{8} ) ^{2}} d x

\int \frac{- 10}{x ^{2} - 10 x} d x

\int \frac{- 7}{1 - x ^{2}} d x

What is the integral of x/((49-x^2)^{3/2)} ?
The integral of x/((49-x^2)^{3/2)} is 1/((49-x^2)^{1/2)}+C