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Popular >

integral of x^3+3x

Solution

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

Solution

\frac{x ^{4}}{4} + \frac{3 x ^{2}}{2} + C

Solution steps

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

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

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

= \frac{x ^{4}}{4} + \frac{3 x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{4}}{4} + \frac{3 x ^{2}}{2} + C

Graph

Popular Examples

integral of (arccos(x))/((1-x^2)^{3/2)}

\int \frac{arccos ( x )}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

integral of x^2-3sqrt(x)

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

integral of 1/((x^2+x)(x^2+9))

\int \frac{1}{( x ^{2} + x ) ( x ^{2} + 9 )} d x

integral of 4(cos(x))^2

\int 4 (cos (x))^{2} d x

integral of 1/(sin(x)+2cos(x)+3)

\int \frac{1}{sin ( x ) + 2 cos ( x ) + 3} d x

Frequently Asked Questions (FAQ)

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