What is the integral of (sin(1/(x^7)))/(x^8) ?

The integral of (sin(1/(x^7)))/(x^8) is 1/7 cos(1/(x^7))+C

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integral of (sin(1/(x^7)))/(x^8)

\int \frac{sin ( \frac{1}{x ^{7}} )}{x ^{8}} d x

\frac{1}{7} cos (\frac{1}{x ^{7}}) + C

Solution steps

\int \frac{sin ( \frac{1}{x ^{7}} )}{x ^{8}} d x

Apply u-substitution

: \int \frac{sin ( \frac{1}{u} )}{7 u ^{2}} d u

= \int \frac{sin ( \frac{1}{u} )}{7 u ^{2}} d u

Take the constant out:

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

= \frac{1}{7} \cdot \int \frac{sin ( \frac{1}{u} )}{u ^{2}} d u

Apply u-substitution

: \int - sin (v) d v

= \frac{1}{7} \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}{7} (- \int sin (v) d v)

Use the common integral:

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

= \frac{1}{7} (- (- cos (v)))

Substitute back

= \frac{1}{7} (- (- cos (\frac{1}{x ^{7}})))

Simplify

= \frac{1}{7} cos (\frac{1}{x ^{7}})

Add a constant to the solution

= \frac{1}{7} cos (\frac{1}{x ^{7}}) + C

\int \frac{sin ^{7} ( 7 x )}{cos ^{4} ( 7 x )} d x

ln (12 x)

\frac{d}{d x} (sin (\frac{π x}{5}))

y = \frac{6 x}{3 - cot ( x )}

\frac{d}{d x} (tan^{2} (\frac{x}{2}))

What is the integral of (sin(1/(x^7)))/(x^8) ?
The integral of (sin(1/(x^7)))/(x^8) is 1/7 cos(1/(x^7))+C