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Popular >

integral of 4x-4x^3

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Popular Examples

integral of 2y^{-2}

\int 2 y^{- 2} d y

integral of 10+(500)/(x+1)

\int 10 + \frac{500}{x + 1} d x

integral of (2x^4-3x^3+5)/(7x^2)

\int \frac{2 x ^{4} - 3 x ^{3} + 5}{7 x ^{2}} d x

integral of tan^{21}(x)sec^{22}(x)

\int tan^{21} (x) sec^{22} (x) d x

integral of 3/(1+2x)

\int \frac{3}{1 + 2 x} d x

Frequently Asked Questions (FAQ)

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