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

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

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integral of x^3sin(x^4)

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

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

Solution steps

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

Apply u-substitution

: \int \frac{sin ( u )}{4} d u

= \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 = x^{4}

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

Simplify

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

Add a constant to the solution

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

\int 9 x^{5} e^{8 x^{2}} d x

\frac{\partial}{\partial y} (x^{3} y^{2})

\int cos (3 θ) d θ

x \to - 2 lim (\frac{3 x - 6}{x + 2})

\frac{d}{d x} (\frac{x ^{3}}{2 ( x + 1 ) ^{2}})

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