What is the integral of 7x^{2/5}+8x^{(-4)/5} ?

The integral of 7x^{2/5}+8x^{(-4)/5} is 5x^{7/5}+40x^{1/5}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 7x^{2/5}+8x^{(-4)/5}

\int 7 x^{\frac{2}{5}} + 8 x^{\frac{- 4}{5}} d x

5 x^{\frac{7}{5}} + 40 x^{\frac{1}{5}} + C

Solution steps

\int 7 x^{\frac{2}{5}} + 8 x^{\frac{- 4}{5}} d x

8 x^{\frac{- 4}{5}} = \frac{8}{x ^{\frac{4}{5}}}

= \int 7 x^{\frac{2}{5}} + \frac{8}{x ^{\frac{4}{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 7 x^{\frac{2}{5}} d x + \int \frac{8}{x ^{\frac{4}{5}}} d x

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

\int \frac{8}{x ^{\frac{4}{5}}} d x = 40 x^{\frac{1}{5}}

= 5 x^{\frac{7}{5}} + 40 x^{\frac{1}{5}}

Add a constant to the solution

= 5 x^{\frac{7}{5}} + 40 x^{\frac{1}{5}} + C

\int (2 cos^{2} (x) - 1) d x

\int \frac{x ^{2}}{6 + x} d x

\int 10 x - 4 x^{3} d x

\int k x k x^{2} + 10 d x

\int (16 y^{3} - 3 y^{2} + 2) d y

What is the integral of 7x^{2/5}+8x^{(-4)/5} ?
The integral of 7x^{2/5}+8x^{(-4)/5} is 5x^{7/5}+40x^{1/5}+C