What is the integral of (x^3)/3-2x^2-5x ?

The integral of (x^3)/3-2x^2-5x is (x^4}{12}-\frac{2x^3)/3-(5x^2)/2+C

Popular >

integral of (x^3)/3-2x^2-5x

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

\frac{x ^{4}}{12} - \frac{2 x ^{3}}{3} - \frac{5 x ^{2}}{2} + C

Solution steps

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

\int \frac{x ^{3}}{3} d x = \frac{x ^{4}}{12}

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

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

= \frac{x ^{4}}{12} - \frac{2 x ^{3}}{3} - \frac{5 x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{4}}{12} - \frac{2 x ^{3}}{3} - \frac{5 x ^{2}}{2} + C

\int (e^{\frac{- t}{6}} - e^{\frac{t}{6}})^{2} d t

\int 2 - 2 cos (4 x) d x

\int - 16 cos (4 x) d x

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

\int \frac{ln ( t )}{t ln ( t ^{2} )} d t

What is the integral of (x^3)/3-2x^2-5x ?
The integral of (x^3)/3-2x^2-5x is (x^4}{12}-\frac{2x^3)/3-(5x^2)/2+C