What is the integral of (5x^{3/2}-3) ?

The integral of (5x^{3/2}-3) is 2x^{5/2}-3x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (5x^{3/2}-3)

\int (5 x^{\frac{3}{2}} - 3) d x

2 x^{\frac{5}{2}} - 3 x + C

Solution steps

\int 5 x^{\frac{3}{2}} - 3 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 5 x^{\frac{3}{2}} d x - \int 3 d x

\int 5 x^{\frac{3}{2}} d x = 2 x^{\frac{5}{2}}

\int 3 d x = 3 x

= 2 x^{\frac{5}{2}} - 3 x

Add a constant to the solution

= 2 x^{\frac{5}{2}} - 3 x + C

\int e^{10 x} 5 x d x

\int \frac{1}{sin ^{2} ( x ) - 5 sin ( x ) cos ( x )} d x

\int (e^{1 - 3 x} + 2 cos (\frac{x}{9})) d x

What is the integral of (5x^{3/2}-3) ?
The integral of (5x^{3/2}-3) is 2x^{5/2}-3x+C