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Popular >

integral of x^3(x+2)

Solution

\int x^{3} (x + 2) d x

Solution

\frac{x ^{5}}{5} + \frac{x ^{4}}{2} + C

Solution steps

\int x^{3} (x + 2) d x

Expand

x^{3} (x + 2) : x^{4} + 2 x^{3}

= \int x^{4} + 2 x^{3} 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^{4} d x + \int 2 x^{3} d x

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

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

= \frac{x ^{5}}{5} + \frac{x ^{4}}{2}

Add a constant to the solution

= \frac{x ^{5}}{5} + \frac{x ^{4}}{2} + C

Popular Examples

integral of sin^5(θ)

\int sin^{5} (θ) d θ

integral of sin^{12}(x)cos^7(x)

\int sin^{12} (x) cos^{7} (x) d x

integral of (x^2)/((1-x))

\int \frac{x ^{2}}{( 1 - x )} d x

integral of 5x^{4/3}+4x^{5/4}

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

integral of (6x^4+4)/(x^2)

\int \frac{6 x ^{4} + 4}{x ^{2}} d x

Frequently Asked Questions (FAQ)

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