What is the integral of (2/(sqrt(x))-3xsqrt(x)+2) ?

The integral of (2/(sqrt(x))-3xsqrt(x)+2) is 4sqrt(x)-6/5 x^{5/2}+2x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2/(sqrt(x))-3xsqrt(x)+2)

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

4 x - \frac{6}{5} x^{\frac{5}{2}} + 2 x + C

Solution steps

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

\int \frac{2}{x} d x = 4 x

\int 3 x x d x = \frac{6}{5} x^{\frac{5}{2}}

\int 2 d x = 2 x

= 4 x - \frac{6}{5} x^{\frac{5}{2}} + 2 x

Add a constant to the solution

= 4 x - \frac{6}{5} x^{\frac{5}{2}} + 2 x + C

y = - x^{3} + 2 x^{2} + 1, at x = - 1

y^{^{''}} - 2 a y^{^{'}} + a^{2} y = 0

\int - sin (θ) d θ

\int 3 t^{2} - 2 t d t

\int_{- 1}^{2} 4 x (1 - x^{2}) d x

What is the integral of (2/(sqrt(x))-3xsqrt(x)+2) ?
The integral of (2/(sqrt(x))-3xsqrt(x)+2) is 4sqrt(x)-6/5 x^{5/2}+2x+C