What is the integral of x/7 sqrt(49+x^2) ?

The integral of x/7 sqrt(49+x^2) is 1/21 (49+x^2)^{3/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x/7 sqrt(49+x^2)

\int \frac{x}{7} 49 + x^{2} d x

\frac{1}{21} (49 + x^{2})^{\frac{3}{2}} + C

Solution steps

\int \frac{x}{7} 49 + x^{2} d x

Take the constant out:

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

= \frac{1}{7} \cdot \int x 49 + x^{2} d x

Apply u-substitution

: \int u^{2} d u

= \frac{1}{7} \cdot \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= \frac{1}{7} \cdot \frac{u ^{3}}{3}

Substitute back

u = 49 + x^{2}

= \frac{1}{7} \cdot \frac{( 49 + x ^{2} ) ^{3}}{3}

Simplify

\frac{1}{7} \cdot \frac{( 49 + x ^{2} ) ^{3}}{3} : \frac{1}{21} (49 + x^{2})^{\frac{3}{2}}

= \frac{1}{21} (49 + x^{2})^{\frac{3}{2}}

Add a constant to the solution

= \frac{1}{21} (49 + x^{2})^{\frac{3}{2}} + C

\frac{d}{d x} (e^{- 2 x} - x)

\int (4 x - 3)^{9} d x

\frac{\partial}{\partial y} (y^{3} cos (4 x))

\frac{d}{d x} ((1 + 4 x^{2}) (x - x^{2}))

\int x - y^{3} + y^{2} sin (x) d x

What is the integral of x/7 sqrt(49+x^2) ?
The integral of x/7 sqrt(49+x^2) is 1/21 (49+x^2)^{3/2}+C