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Popular >

integral of x(2x-1)

Solution

\int x (2 x - 1) d x

Solution

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

Solution steps

\int x (2 x - 1) d x

Expand

x (2 x - 1) : 2 x^{2} - x

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

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

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

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

Add a constant to the solution

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

Popular Examples

sum from n=2 to infinity of (n+2)/(2n+3)

n = 2 \sum \infty \frac{n + 2}{2 n + 3}

limit as x approaches 1 of x(2)

x \to 1 lim (x (2))

derivative of ax^2+by(x^2+λ(x^2+y^2-c^2))

\frac{d}{d x} (a x^{2} + b y (x)^{2} + λ (x^{2} + y^{2} - c^{2}))

x^{2} - 2 x y + x y^{^{'}} = 0

integral of (x+4)/(x^2+5x+4)

\int \frac{x + 4}{x ^{2} + 5 x + 4} d x

Frequently Asked Questions (FAQ)

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