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Popular >

integral of 4y-y^3

Solution

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

Solution

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

Solution steps

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

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

\int y^{3} d y = \frac{y ^{4}}{4}

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

Add a constant to the solution

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

Graph

Popular Examples

integral of sqrt(17+4x^2)

\int 17 + 4 x^{2} d x

integral of x^3(3x^4+2)^9

\int x^{3} (3 x^{4} + 2)^{9} d x

integral of x^2-3x^3-10x-1

\int x^{2} - 3 x^{3} - 10 x - 1 d x

integral of 5sin(x^2)

\int 5 sin (x^{2}) d x

integral of (3^x-1)/(3^x+1)

\int \frac{3 ^{x} - 1}{3 ^{x} + 1} d x

Frequently Asked Questions (FAQ)

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