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Popular >

integral of x^2+6x+9

Solution

\int x^{2} + 6 x + 9 d x

Solution

\frac{x ^{3}}{3} + 3 x^{2} + 9 x + C

Solution steps

\int x^{2} + 6 x + 9 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 6 x d x + \int 9 d x

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

\int 6 x d x = 3 x^{2}

\int 9 d x = 9 x

= \frac{x ^{3}}{3} + 3 x^{2} + 9 x

Add a constant to the solution

= \frac{x ^{3}}{3} + 3 x^{2} + 9 x + C

Popular Examples

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\int \frac{1}{2 y ^{2} + c} d y

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\int \frac{( 11 + x )}{x} d x

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\int \frac{1}{( cos ( x ) + 1 )} d x

integral of (8x^3-4csc^2(x)+e^x)

\int (8 x^{3} - 4 csc^{2} (x) + e^{x}) d x

integral of-ln(x^2-1)

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

Frequently Asked Questions (FAQ)

What is the integral of x^2+6x+9 ?
The integral of x^2+6x+9 is (x^3)/3+3x^2+9x+C