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Popular >

integral of x(12x+6)

Solution

\int x (12 x + 6) d x

Solution

4 x^{3} + 3 x^{2} + C

Solution steps

\int x (12 x + 6) d x

Expand

x (12 x + 6) : 12 x^{2} + 6 x

= \int 12 x^{2} + 6 x 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 12 x^{2} d x + \int 6 x d x

\int 12 x^{2} d x = 4 x^{3}

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

= 4 x^{3} + 3 x^{2}

Add a constant to the solution

= 4 x^{3} + 3 x^{2} + C

Popular Examples

integral of 2x^2-4x+5

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

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

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

integral of (x^2+\sqrt[3]{x})^2

integral of (x^3)/(2-x)

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

integral of 5/(xln^3(x))

\int \frac{5}{x ln ^{3} ( x )} d x

Frequently Asked Questions (FAQ)

What is the integral of x(12x+6) ?
The integral of x(12x+6) is 4x^3+3x^2+C