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Popular >

integral of x(x^3-1)

Solution

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

Solution

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

Solution steps

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

Expand

x (x^{3} - 1) : x^{4} - x

= \int x^{4} - 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 x^{4} d x - \int x d x

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

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

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

Add a constant to the solution

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

Popular Examples

integral of 1/(x^5)

\int \frac{1}{x ^{5}} d x

integral of (1+x)/(4+2x+x^2)

\int \frac{1 + x}{4 + 2 x + x ^{2}} d x

limit as q approaches-11+of ln(q+11)

q \to - 11 + lim (ln (q + 11))

integral of (sin(ln(8x)))/x

\int \frac{sin ( ln ( 8 x ) )}{x} d x

(\partial)/(\partial x)(2e^{-2x}+1/3 e^x)

\frac{\partial}{\partial x} (2 e^{- 2 x} + \frac{1}{3} e^{x})

Frequently Asked Questions (FAQ)

What is the integral of x(x^3-1) ?
The integral of x(x^3-1) is (x^5)/5-(x^2)/2+C