What is the integral of (3x^5-8x^3+2) ?

The integral of (3x^5-8x^3+2) is (x^6)/2-2x^4+2x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (3x^5-8x^3+2)

\int (3 x^{5} - 8 x^{3} + 2) d x

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

Solution steps

\int 3 x^{5} - 8 x^{3} + 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 3 x^{5} d x - \int 8 x^{3} d x + \int 2 d x

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

\int 8 x^{3} d x = 2 x^{4}

\int 2 d x = 2 x

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

Add a constant to the solution

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

\int \frac{( x ^{3} - x ^{4} ) ^{2}}{x} d x

\int \frac{x}{2} e^{- \frac{3 x}{4}} d x

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

\int t^{2} e^{6 t} d t

\int \frac{2 x - 18}{x + 3} d x

What is the integral of (3x^5-8x^3+2) ?
The integral of (3x^5-8x^3+2) is (x^6)/2-2x^4+2x+C