What is the integral of (sin(1/(x^4)))/(x^5) ?

The integral of (sin(1/(x^4)))/(x^5) is 1/4 cos(1/(x^4))+C

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integral of (sin(1/(x^4)))/(x^5)

\int \frac{sin ( \frac{1}{x ^{4}} )}{x ^{5}} d x

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

Solution steps

\int \frac{sin ( \frac{1}{x ^{4}} )}{x ^{5}} d x

Apply u-substitution

: \int \frac{sin ( \frac{1}{u} )}{4 u ^{2}} d u

= \int \frac{sin ( \frac{1}{u} )}{4 u ^{2}} 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 \frac{sin ( \frac{1}{u} )}{u ^{2}} d u

Apply u-substitution

: \int - sin (v) d v

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

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

Simplify

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

Add a constant to the solution

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

\int_{0.2}^{0.4} 150 x d x

\frac{5}{x + 5}

y^{^{'}} - (2 x + 1) y = 0

\int \frac{1}{csc ( x ) ( 1 + sin ( x ) )} d x

\int_{0}^{x} 1 + 36 t d t

What is the integral of (sin(1/(x^4)))/(x^5) ?
The integral of (sin(1/(x^4)))/(x^5) is 1/4 cos(1/(x^4))+C