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Popular >

integral of (x^3+5x)

Solution

\int (x^{3} + 5 x) d x

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Popular Examples

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

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

integral of (1/x+1)

\int (\frac{1}{x} + 1) d x

integral of x(5x^2-6)^4

\int x (5 x^{2} - 6)^{4} d x

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

\int \frac{2}{x ( 1 + x )} d x

integral of (x-18)/(4x^3+9x)

\int \frac{x - 18}{4 x ^{3} + 9 x} d x

Frequently Asked Questions (FAQ)

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