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

: \frac{y ^{2}}{2}

= 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

\frac{1}{( s \cdot ( s ^{2} + 0.4 s + 4 ) )}

\int 4 x y (x^{2} + y^{2})^{0.5} d x

9 x + 7

\int \frac{3 x - 4}{( x - 1 ) ^{2}} d x

g (t) = 2 t^{- \frac{1}{4}}

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