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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 (x^3-2x-4)/(x^2-2x)

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

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\int 3 x ln (x) d x

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\int (200 e^{0.1 t} + 150 e^{- 0.3 t}) d t

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\int \frac{sin ^{2} ( x ) + cos ^{2} ( x )}{csc ( x )} d x

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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