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

The integral of (2x^3-3)^2x is (x^8)/2-(12x^5)/5+(9x^2)/2+C

Popular >

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

\int (2 x^{3} - 3)^{2} x d x

\frac{x ^{8}}{2} - \frac{12 x ^{5}}{5} + \frac{9 x ^{2}}{2} + C

Solution steps

\int (2 x^{3} - 3)^{2} x d x

Expand

(2 x^{3} - 3)^{2} x : 4 x^{7} - 12 x^{4} + 9 x

= \int 4 x^{7} - 12 x^{4} + 9 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 4 x^{7} d x - \int 12 x^{4} d x + \int 9 x d x

\int 4 x^{7} d x = \frac{x ^{8}}{2}

\int 12 x^{4} d x = \frac{12 x ^{5}}{5}

\int 9 x d x = \frac{9 x ^{2}}{2}

= \frac{x ^{8}}{2} - \frac{12 x ^{5}}{5} + \frac{9 x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{8}}{2} - \frac{12 x ^{5}}{5} + \frac{9 x ^{2}}{2} + C

\int \frac{2}{x ^{2} 25 - x ^{2}} d x

\int \frac{x + 2}{x ^{2} - 25} d x

\int (\frac{2 x ^{2} - 6 x + 1}{x ^{2}}) d x

\int 2 e^{x^{2} + l n (x)} (2 x + x^{- 1}) d x

\int \frac{x + 22}{( x + 7 ) ( x - 8 )} d x

What is the integral of (2x^3-3)^2x ?
The integral of (2x^3-3)^2x is (x^8)/2-(12x^5)/5+(9x^2)/2+C