What is the integral of (4x^5+1)x^4 ?

The integral of (4x^5+1)x^4 is (2x^{10})/5+(x^5)/5+C

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integral of (4x^5+1)x^4

\int (4 x^{5} + 1) x^{4} d x

\frac{2 x ^{10}}{5} + \frac{x ^{5}}{5} + C

Solution steps

\int (4 x^{5} + 1) x^{4} d x

Expand

(4 x^{5} + 1) x^{4} : 4 x^{9} + x^{4}

= \int 4 x^{9} + 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 4 x^{9} d x + \int x^{4} d x

\int 4 x^{9} d x = \frac{2 x ^{10}}{5}

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

= \frac{2 x ^{10}}{5} + \frac{x ^{5}}{5}

Add a constant to the solution

= \frac{2 x ^{10}}{5} + \frac{x ^{5}}{5} + C

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What is the integral of (4x^5+1)x^4 ?
The integral of (4x^5+1)x^4 is (2x^{10})/5+(x^5)/5+C