What is the integral of x^3tan(x)y ?

The integral of x^3tan(x)y is (x^3)/2 y^2tan(x)+C

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integral of x^3tan(x)y

\int x^{3} tan (x) y d y

\frac{x ^{3}}{2} y^{2} tan (x) + C

Solution steps

\int x^{3} tan (x) y d y

Take the constant out:

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

= tan (x) x^{3} \cdot \int y d y

Apply the Power Rule

= tan (x) x^{3} \frac{y ^{2}}{2}

Simplify

tan (x) x^{3} \frac{y ^{2}}{2} : \frac{x ^{3}}{2} y^{2} tan (x)

= \frac{x ^{3}}{2} y^{2} tan (x)

Add a constant to the solution

= \frac{x ^{3}}{2} y^{2} tan (x) + C

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