What is the integral of (5-x)sqrt(x) ?

The integral of (5-x)sqrt(x) is 10/3 x^{3/2}-2/5 x^{5/2}+C

Popular >

integral of (5-x)sqrt(x)

\int (5 - x) x d x

\frac{10}{3} x^{\frac{3}{2}} - \frac{2}{5} x^{\frac{5}{2}} + C

Solution steps

\int (5 - x) x d x

Expand

(5 - x) x : 5 x - x^{\frac{3}{2}}

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

\int 5 x d x = \frac{10}{3} x^{\frac{3}{2}}

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

= \frac{10}{3} x^{\frac{3}{2}} - \frac{2}{5} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{10}{3} x^{\frac{3}{2}} - \frac{2}{5} x^{\frac{5}{2}} + C

\int 2 x + 10 d x

\int \frac{x ^{3} + 2 x ^{2} + x + 1}{x ^{2} + 2 x} d x

\int cos (θ) sin^{9} (θ) d θ

\int sec (2 t) d t

\int \frac{x ^{2} + 2 x + 3}{x ^{2} + 4 x + 13} d x

What is the integral of (5-x)sqrt(x) ?
The integral of (5-x)sqrt(x) is 10/3 x^{3/2}-2/5 x^{5/2}+C