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Popular >

integral of x^2+3x-1

Solution

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

Solution

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

Solution steps

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

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

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

\int 1 d x = x

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

Add a constant to the solution

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

Graph

Popular Examples

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\int (x + 1)^{2} \cdot e^{x} d x

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

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

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

integral of 3/7 x^{7/4}

\int \frac{3}{7} x^{\frac{7}{4}} d x

Frequently Asked Questions (FAQ)

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