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Popular >

integral of (x^2+5x)

Solution

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

Solution

\frac{x ^{3}}{3} + \frac{5 x ^{2}}{2} + C

Solution steps

\int x^{2} + 5 x 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^{2} d x + \int 5 x d x

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

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

= \frac{x ^{3}}{3} + \frac{5 x ^{2}}{2}

Add a constant to the solution

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

Popular Examples

integral of sec(8-x)tan(8-x)

\int sec (8 - x) tan (8 - x) d x

integral of (4x^3+11)/((x^2+2)^2)

\int \frac{4 x ^{3} + 11}{( x ^{2} + 2 ) ^{2}} d x

integral of (4x^2)/(x+1)

\int \frac{4 x ^{2}}{x + 1} d x

integral of sqrt(9-3y)

\int 9 - 3 y d y

integral of e^{3x}(3)

\int e^{3 x} (3) d x

Frequently Asked Questions (FAQ)

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