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Popular >

integral of-2x^2+x

Solution

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

Solution

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

Solution steps

\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

integral of x^3(x^4+3)

\int x^{3} (x^{4} + 3) d x

integral of csc^6(x)cot(x)

\int csc^{6} (x) cot (x) d x

integral of 1/(2t-1)

\int \frac{1}{2 t - 1} d t

integral of (4x-5)^{2/3}

\int (4 x - 5)^{\frac{2}{3}} d x

integral of (1+6x^2-10x^4)

\int (1 + 6 x^{2} - 10 x^{4}) d x

Frequently Asked Questions (FAQ)

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