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Popular >

integral of (3x+2)(x+3)

Solution

\int (3 x + 2) (x + 3) d x

Solution

x^{3} + \frac{11 x ^{2}}{2} + 6 x + C

Solution steps

\int (3 x + 2) (x + 3) d x

Expand

(3 x + 2) (x + 3) : 3 x^{2} + 11 x + 6

= \int 3 x^{2} + 11 x + 6 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 3 x^{2} d x + \int 11 x d x + \int 6 d x

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

\int 11 x d x = \frac{11 x ^{2}}{2}

\int 6 d x = 6 x

= x^{3} + \frac{11 x ^{2}}{2} + 6 x

Add a constant to the solution

= x^{3} + \frac{11 x ^{2}}{2} + 6 x + C

Popular Examples

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

integral of (x^3-x^2+1)

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

integral of (e^{3x})/(e^x+1)

\int \frac{e ^{3 x}}{e ^{x} + 1} d x

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

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

integral of (ln(tan(x)))/(sin(2x))

\int \frac{ln ( tan ( x ) )}{sin ( 2 x )} d x

Frequently Asked Questions (FAQ)

What is the integral of (3x+2)(x+3) ?
The integral of (3x+2)(x+3) is x^3+(11x^2)/2+6x+C