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Popular >

integral of 2x^2-x+1

Solution

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

Solution

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

Solution steps

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

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

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

\int 1 d x = x

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

Add a constant to the solution

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

Popular Examples

integral of 1/(sqrt(P))

\int \frac{1}{P} d P

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

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

integral of (1-x)/(x+1)

\int \frac{1 - x}{x + 1} d x

integral of 2xsin(-4x+3)

\int 2 x sin (- 4 x + 3) d x

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

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

Frequently Asked Questions (FAQ)

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