What is the integral of 3x^5-8x^4 ?

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

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integral of 3x^5-8x^4

integral

3 x^{5} - 8 x^{4}

\frac{x ^{6}}{2} - \frac{8 x ^{5}}{5} + C

Solution steps

\int 3 x^{5} - 8 x^{4} 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^{4} d x

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

\int 8 x^{4} d x = \frac{8 x ^{5}}{5}

= \frac{x ^{6}}{2} - \frac{8 x ^{5}}{5}

Add a constant to the solution

= \frac{x ^{6}}{2} - \frac{8 x ^{5}}{5} + C

\frac{2 x ^{2}}{( x ^{2} + 1 )}

2 - x^{2}

\frac{( 6 x + 1 )}{( 2 x - 3 )}

\frac{9}{( 3 x - 4 ) ^{2}}

x^{5} cos (3 x)

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