What is the integral of (cos(pi/(x^{33)}))/(x^{34)} ?

The integral of (cos(pi/(x^{33)}))/(x^{34)} is -1/(33pi)sin(pi/(x^{33)})+C

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integral of (cos(pi/(x^{33)}))/(x^{34)}

\int \frac{cos ( \frac{π}{x ^{33}} )}{x ^{34}} d x

- \frac{1}{33 π} sin (\frac{π}{x ^{33}}) + C

Solution steps

\int \frac{cos ( \frac{π}{x ^{33}} )}{x ^{34}} d x

Apply u-substitution

: \int \frac{cos ( \frac{π}{u} )}{33 u ^{2}} d u

= \int \frac{cos ( \frac{π}{u} )}{33 u ^{2}} d u

Take the constant out:

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

= \frac{1}{33} \cdot \int \frac{cos ( \frac{π}{u} )}{u ^{2}} d u

Apply u-substitution

: \int - \frac{cos ( v )}{π} d v

= \frac{1}{33} \cdot \int - \frac{cos ( v )}{π} d v

Take the constant out:

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

= \frac{1}{33} (- \frac{1}{π} \cdot \int cos (v) d v)

Use the common integral:

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

= \frac{1}{33} (- \frac{1}{π} sin (v))

Substitute back

= \frac{1}{33} (- \frac{1}{π} sin (\frac{π}{x ^{33}}))

Simplify

\frac{1}{33} (- \frac{1}{π} sin (\frac{π}{x ^{33}})) : - \frac{1}{33 π} sin (\frac{π}{x ^{33}})

= - \frac{1}{33 π} sin (\frac{π}{x ^{33}})

Add a constant to the solution

= - \frac{1}{33 π} sin (\frac{π}{x ^{33}}) + C

\frac{\partial}{\partial x} (\frac{1}{x - 1})

\frac{\partial}{\partial x} (e^{\frac{x y}{z}})

\frac{e ^{x}}{cos ( x )}

\int sin (3 z) cos^{2} (3 z) d z

What is the integral of (cos(pi/(x^{33)}))/(x^{34)} ?
The integral of (cos(pi/(x^{33)}))/(x^{34)} is -1/(33pi)sin(pi/(x^{33)})+C