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Popular Calculus >

integral of x-4x^3

Solution

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

Solution

\frac{x ^{2}}{2} - x^{4} + C

Solution steps

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

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

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

= \frac{x ^{2}}{2} - x^{4}

Add a constant to the solution

= \frac{x ^{2}}{2} - x^{4} + C

Graph

Popular Examples

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\int \frac{1}{( 4 - x ^{2} ) ^{1.5}} d x

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\int (- 12 x y^{2} + 8 x^{3} y + 3) d x

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

integral of (2x+4)/((x^2-5x+6))

\int \frac{2 x + 4}{( x ^{2} - 5 x + 6 )} d x

integral of tanh^3(x)

\int tanh^{3} (x) d x

Frequently Asked Questions (FAQ)

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