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Popular Calculus >

integral of (y^5-5y)

Solution

\int (y^{5} - 5 y) d y

Solution

\frac{y ^{6}}{6} - \frac{5 y ^{2}}{2} + C

Solution steps

\int y^{5} - 5 y 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 y^{5} d y - \int 5 y d y

\int y^{5} d y = \frac{y ^{6}}{6}

\int 5 y d y = \frac{5 y ^{2}}{2}

= \frac{y ^{6}}{6} - \frac{5 y ^{2}}{2}

Add a constant to the solution

= \frac{y ^{6}}{6} - \frac{5 y ^{2}}{2} + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of (y^5-5y) ?
The integral of (y^5-5y) is (y^6)/6-(5y^2)/2+C