What is the integral of (x+7)sqrt(14x+x^2) ?

The integral of (x+7)sqrt(14x+x^2) is 1/3 (14x+x^2)^{3/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (x+7)sqrt(14x+x^2)

\int (x + 7) 14 x + x^{2} d x

\frac{1}{3} (14 x + x^{2})^{\frac{3}{2}} + C

Solution steps

\int (x + 7) 14 x + x^{2} d x

Apply u-substitution

= \int u^{2} d u

Apply the Power Rule

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

Substitute back

u = 14 x + x^{2}

= \frac{( 14 x + x ^{2} ) ^{3}}{3}

Simplify

\frac{( 14 x + x ^{2} ) ^{3}}{3} : \frac{1}{3} (14 x + x^{2})^{\frac{3}{2}}

= \frac{1}{3} (14 x + x^{2})^{\frac{3}{2}}

Add a constant to the solution

= \frac{1}{3} (14 x + x^{2})^{\frac{3}{2}} + C

\int x \cdot 7^{x^{2}} d x

\int e^{x} + e^{a x} + e^{a x + b} d x

\int - \frac{1}{1 + x} d x

\int cos (x) + \frac{1}{3} x d x

\int e^{x} (x) d x

What is the integral of (x+7)sqrt(14x+x^2) ?
The integral of (x+7)sqrt(14x+x^2) is 1/3 (14x+x^2)^{3/2}+C