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Popular >

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

Popular Examples

y^{''}+y=0,y(pi/3)=16,y^'(pi/3)=-32

y^{^{''}} + y = 0, y (\frac{π}{3}) = 16, y^{^{'}} (\frac{π}{3}) = - 32

(\partial)/(\partial y)(7e^{x^2ln(y)})

\frac{\partial}{\partial y} (7 e^{x^{2} l n (y)})

derivative of 5Y^{5/8}X^{3/8}derivative of

5 Y^{\frac{5}{8}} X^{\frac{3}{8}}

integral of 1/(3x+12)

\int \frac{1}{3 x + 12} d x

(\partial)/(\partial y)(e^{x+y+4})

\frac{\partial}{\partial y} (e^{x + y + 4})

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