What is the integral of x^5+7sqrt(x) ?

The integral of x^5+7sqrt(x) is (x^6)/6+14/3 x^{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^5+7sqrt(x)

\int x^{5} + 7 x d x

\frac{x ^{6}}{6} + \frac{14}{3} x^{\frac{3}{2}} + C

Solution steps

\int x^{5} + 7 x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x^{5} d x + \int 7 x d x

\int x^{5} d x = \frac{x ^{6}}{6}

\int 7 x d x = \frac{14}{3} x^{\frac{3}{2}}

= \frac{x ^{6}}{6} + \frac{14}{3} x^{\frac{3}{2}}

Add a constant to the solution

= \frac{x ^{6}}{6} + \frac{14}{3} x^{\frac{3}{2}} + C

\int 8 x e^{5 x^{2}} d x

\int \frac{x ^{2} + 47}{x ^{2} + 49} d x

\int sin (x) e^{- 3 x} d x

\int \frac{x ^{2} + 2 x - 1}{x ^{3} + x ^{2} + x + 1} d x

\int \frac{2 x}{y ^{3}} d x

What is the integral of x^5+7sqrt(x) ?
The integral of x^5+7sqrt(x) is (x^6)/6+14/3 x^{3/2}+C