What is the integral of sqrt(x^5)+\sqrt[5]{x^7} ?

The integral of sqrt(x^5)+\sqrt[5]{x^7} is 2/7 x^{7/2}+5/12 x^{12/5}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sqrt(x^5)+\sqrt[5]{x^7}

\frac{2}{7} x^{\frac{7}{2}} + \frac{5}{12} x^{\frac{12}{5}} + C

Solution steps

Simplify

= \int x^{\frac{5}{2}} + x^{\frac{7}{5}} 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^{\frac{5}{2}} d x + \int x^{\frac{7}{5}} d x

\int x^{\frac{5}{2}} d x = \frac{2}{7} x^{\frac{7}{2}}

\int x^{\frac{7}{5}} d x = \frac{5}{12} x^{\frac{12}{5}}

= \frac{2}{7} x^{\frac{7}{2}} + \frac{5}{12} x^{\frac{12}{5}}

Add a constant to the solution

= \frac{2}{7} x^{\frac{7}{2}} + \frac{5}{12} x^{\frac{12}{5}} + C

\int 2 arctan (4 y) d y

\int x^{5} \cdot e^{- x^{3}} d x

\int e^{- x^{9}} d x

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

What is the integral of sqrt(x^5)+\sqrt[5]{x^7} ?
The integral of sqrt(x^5)+\sqrt[5]{x^7} is 2/7 x^{7/2}+5/12 x^{12/5}+C