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{e ^{3 x}}{( 1 + e ^{x} ) ^{3}} d x

\int \frac{1}{4 sec ( x ) + 5} d x

\int \frac{16 + x ^{2}}{x ^{2}} d x

\int \frac{x ln ( sin ( x ^{2} ) )}{tan ( x ^{2} )} d x

\int \frac{x + 5}{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