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

The integral of x(3x^3-2) is 3/2 x^5-x^2-(9x^5)/(10)+C

Popular >

integral of x(3x^3-2)

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

\frac{3}{2} x^{5} - x^{2} - \frac{9 x ^{5}}{10} + C

Solution steps

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

Apply Integration By Parts

: \frac{1}{2} x^{2} (3 x^{3} - 2) - \int \frac{9 x ^{4}}{2} d x

= \frac{1}{2} x^{2} (3 x^{3} - 2) - \int \frac{9 x ^{4}}{2} d x

\int \frac{9 x ^{4}}{2} d x = \frac{9 x ^{5}}{10}

= \frac{1}{2} x^{2} (3 x^{3} - 2) - \frac{9 x ^{5}}{10}

Expand

\frac{1}{2} x^{2} (3 x^{3} - 2) : \frac{3}{2} x^{5} - x^{2}

= \frac{3}{2} x^{5} - x^{2} - \frac{9 x ^{5}}{10}

Add a constant to the solution

= \frac{3}{2} x^{5} - x^{2} - \frac{9 x ^{5}}{10} + C

\int \frac{tan ( x ) + cos ( x )}{sin ( 2 x )} d x

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

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

\int \frac{4}{5 t + 2} d t

\int cos^{2} (t) sin^{5} (d) t

What is the integral of x(3x^3-2) ?
The integral of x(3x^3-2) is 3/2 x^5-x^2-(9x^5)/(10)+C