What is the integral of xsqrt(49+x^2) ?

The integral of xsqrt(49+x^2) is 1/3 (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 xsqrt(49+x^2)

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

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

Solution steps

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

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

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

= \frac{u ^{3}}{3}

Substitute back

u = 49 + x^{2}

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

Simplify

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

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

Add a constant to the solution

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

\int x e^{- 2.1 x} d x

\int (x^{2} cos (x^{3})) d x

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

\int \frac{1}{x ( ln ( x ) + 4 ) ^{5}} d x

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

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