What is the integral of (4x^5-3x^4-25) ?

The integral of (4x^5-3x^4-25) is (2x^6)/3-(3x^5)/5-25x+C

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integral of (4x^5-3x^4-25)

\int (4 x^{5} - 3 x^{4} - 25) d x

\frac{2 x ^{6}}{3} - \frac{3 x ^{5}}{5} - 25 x + C

Solution steps

\int 4 x^{5} - 3 x^{4} - 25 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^{5} d x - \int 3 x^{4} d x - \int 25 d x

\int 4 x^{5} d x = \frac{2 x ^{6}}{3}

\int 3 x^{4} d x = \frac{3 x ^{5}}{5}

\int 25 d x = 25 x

= \frac{2 x ^{6}}{3} - \frac{3 x ^{5}}{5} - 25 x

Add a constant to the solution

= \frac{2 x ^{6}}{3} - \frac{3 x ^{5}}{5} - 25 x + C

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What is the integral of (4x^5-3x^4-25) ?
The integral of (4x^5-3x^4-25) is (2x^6)/3-(3x^5)/5-25x+C