What is the integral of (sin(5)y^2)5y ?

The integral of (sin(5)y^2)5y is 5/4 sin(5)y^4+C

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integral of (sin(5)y^2)5y

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

\frac{5}{4} sin (5) y^{4} + C

Solution steps

\int sin (5) y^{2} \cdot 5 y d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= sin (5) \cdot 5 \cdot \int y^{2} y d y

Simplify

y^{2} y : y^{3}

= sin (5) \cdot 5 \cdot \int y^{3} d y

Apply the Power Rule

: \frac{y ^{4}}{4}

= sin (5) \cdot 5 \cdot \frac{y ^{4}}{4}

Simplify

sin (5) \cdot 5 \cdot \frac{y ^{4}}{4} : \frac{5}{4} sin (5) y^{4}

= \frac{5}{4} sin (5) y^{4}

Add a constant to the solution

= \frac{5}{4} sin (5) y^{4} + C

\int \frac{csc ( 2 x )}{x} d x

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

\int 5 x^{2} - 3 x d x

\int \frac{1 - x}{x ^{2} + 2 x - 4} d x

\int u^{2} 1 - u^{3} d u

What is the integral of (sin(5)y^2)5y ?
The integral of (sin(5)y^2)5y is 5/4 sin(5)y^4+C