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Popular >

integral of x^2(x-5)

Solution

\int x^{2} (x - 5) d x

Solution

\frac{x ^{4}}{4} - \frac{5 x ^{3}}{3} + C

Solution steps

\int x^{2} (x - 5) d x

Expand

x^{2} (x - 5) : x^{3} - 5 x^{2}

= \int x^{3} - 5 x^{2} 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^{3} d x - \int 5 x^{2} d x

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

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

= \frac{x ^{4}}{4} - \frac{5 x ^{3}}{3}

Add a constant to the solution

= \frac{x ^{4}}{4} - \frac{5 x ^{3}}{3} + C

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\int x^{4} \cdot e^{- x} d x

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\int \frac{ln ( 6 x )}{x [ ln ( 3 x ) ] ^{- 2}} d x

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Frequently Asked Questions (FAQ)

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