What is the integral of (3x^5-5x+6) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (3x^5-5x+6)

\int (3 x^{5} - 5 x + 6) d x

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

Solution steps

\int 3 x^{5} - 5 x + 6 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 5 x d x + \int 6 d x

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

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

\int 6 d x = 6 x

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

Add a constant to the solution

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

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