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Popular >

integral of 12x-12x^3

Solution

\int 12 x - 12 x^{3} d x

Solution

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

Solution steps

\int 12 x - 12 x^{3} 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 d x - \int 12 x^{3} d x

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

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

= 6 x^{2} - 3 x^{4}

Add a constant to the solution

= 6 x^{2} - 3 x^{4} + C

Graph

Popular Examples

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\int (x + 1)^{10} (x + 5) d x

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

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\int \frac{x + 10}{x ^{2} + 3 x + 2} d x

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\int 2 cos (2 x) - 6 d x

integral of 1/(x^2-10x+9)

\int \frac{1}{x ^{2} - 10 x + 9} d x

Frequently Asked Questions (FAQ)

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