What is the integral of x^3sin(2-x^4) ?

The integral of x^3sin(2-x^4) is 1/4 cos(2-x^4)+C

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integral of x^3sin(2-x^4)

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

\frac{1}{4} cos (2 - x^{4}) + C

Solution steps

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

Apply u-substitution

= \int - \frac{sin ( u )}{4} d u

Take the constant out:

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

= - \frac{1}{4} \cdot \int sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= - \frac{1}{4} (- cos (u))

Substitute back

u = 2 - x^{4}

= - \frac{1}{4} (- cos (2 - x^{4}))

Simplify

= \frac{1}{4} cos (2 - x^{4})

Add a constant to the solution

= \frac{1}{4} cos (2 - x^{4}) + C

What is the integral of x^3sin(2-x^4) ?
The integral of x^3sin(2-x^4) is 1/4 cos(2-x^4)+C