What is the integral of [u^5-u^3+u^2] ?

The integral of [u^5-u^3+u^2] is (u^6)/6-(u^4)/4+(u^3)/3+C

Popular >

integral of [u^5-u^3+u^2]

\int [u^{5} - u^{3} + u^{2}] d u

\frac{u ^{6}}{6} - \frac{u ^{4}}{4} + \frac{u ^{3}}{3} + C

Solution steps

\int u^{5} - u^{3} + u^{2} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u^{5} d u - \int u^{3} d u + \int u^{2} d u

\int u^{5} d u = \frac{u ^{6}}{6}

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

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

= \frac{u ^{6}}{6} - \frac{u ^{4}}{4} + \frac{u ^{3}}{3}

Add a constant to the solution

= \frac{u ^{6}}{6} - \frac{u ^{4}}{4} + \frac{u ^{3}}{3} + C

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

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

\int t sin (t) cos (2 t) d t

\int 18 (x^{2} + 1) (x^{3} + 3 x)^{2} d x

\int \frac{5}{2 x} sin (2 x) d x

What is the integral of [u^5-u^3+u^2] ?
The integral of [u^5-u^3+u^2] is (u^6)/6-(u^4)/4+(u^3)/3+C