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Popular >

integral of (4x-8y^3)

Solution

\int (4 x - 8 y^{3}) d y

Solution

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

Solution steps

\int 4 x - 8 y^{3} d y

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 y - \int 8 y^{3} d y

\int 4 x d y = 4 x y

\int 8 y^{3} d y = 2 y^{4}

= 4 x y - 2 y^{4}

Add a constant to the solution

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

Graph

Popular Examples

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

y^{''}-2y^'+y=24x^2e^x

y^{^{''}} - 2 y^{^{'}} + y = 24 x^{2} e^{x}

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integral of x/t

\int \frac{x}{t} d t

Frequently Asked Questions (FAQ)

What is the integral of (4x-8y^3) ?
The integral of (4x-8y^3) is 4xy-2y^4+C