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Popular Calculus >

integral of x^5-3x+8

Solution

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

Solution

\frac{x ^{6}}{6} - \frac{3 x ^{2}}{2} + 8 x + C

Solution steps

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

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

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

\int 8 d x = 8 x

= \frac{x ^{6}}{6} - \frac{3 x ^{2}}{2} + 8 x

Add a constant to the solution

= \frac{x ^{6}}{6} - \frac{3 x ^{2}}{2} + 8 x + C

Graph

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\int \frac{x ^{2} + 47}{x ^{2} + 49} d x

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\int sin (x) e^{- 3 x} d x

Frequently Asked Questions (FAQ)

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