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Popular >

integral of x^2+3x-4

Solution

\int x^{2} + 3 x - 4 d x

Solution

\frac{x ^{3}}{3} + \frac{3 x ^{2}}{2} - 4 x + C

Solution steps

\int x^{2} + 3 x - 4 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 4 d x

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

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

\int 4 d x = 4 x

= \frac{x ^{3}}{3} + \frac{3 x ^{2}}{2} - 4 x

Add a constant to the solution

= \frac{x ^{3}}{3} + \frac{3 x ^{2}}{2} - 4 x + C

Popular Examples

integral of sqrt(2)x

\int 2 x d x

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\int x^{3} (1 - 4 x^{2})^{\frac{3}{2}} d x

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integral of 8/(x^3-4x)

\int \frac{8}{x ^{3} - 4 x} d x

integral of (2y+6)/(y+3)

\int \frac{2 y + 6}{y + 3} d y

Frequently Asked Questions (FAQ)

What is the integral of x^2+3x-4 ?
The integral of x^2+3x-4 is (x^3)/3+(3x^2)/2-4x+C