What is the integral of (u+3)(8u+5) ?

The integral of (u+3)(8u+5) is (8u^3)/3+(29u^2)/2+15u+C

Popular >

integral of (u+3)(8u+5)

\int (u + 3) (8 u + 5) d u

\frac{8 u ^{3}}{3} + \frac{29 u ^{2}}{2} + 15 u + C

Solution steps

\int (u + 3) (8 u + 5) d u

Expand

(u + 3) (8 u + 5) : 8 u^{2} + 29 u + 15

= \int 8 u^{2} + 29 u + 15 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 8 u^{2} d u + \int 29 u d u + \int 15 d u

\int 8 u^{2} d u = \frac{8 u ^{3}}{3}

\int 29 u d u = \frac{29 u ^{2}}{2}

\int 15 d u = 15 u

= \frac{8 u ^{3}}{3} + \frac{29 u ^{2}}{2} + 15 u

Add a constant to the solution

= \frac{8 u ^{3}}{3} + \frac{29 u ^{2}}{2} + 15 u + C

\int \frac{e ^{4 x}}{( e ^{2 x} - 1 ) ^{3}} d x

\frac{d}{d x} (ln (\frac{3}{x}))

x \to 2 + lim (\frac{1}{( x - 2 ) ^{3}})

x \to 0 lim (\frac{x}{x ^{2} - 4 x})

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

What is the integral of (u+3)(8u+5) ?
The integral of (u+3)(8u+5) is (8u^3)/3+(29u^2)/2+15u+C