What is the integral of sin(x-2nx) ?

The integral of sin(x-2nx) is -1/(1-2n)cos(x-2nx)+C

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integral of sin(x-2nx)

\int sin (x - 2 n x) d x

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

Solution steps

\int sin (x - 2 n x) d x

Apply u-substitution

: \int \frac{sin ( u )}{1 - 2 n} d u

= \int \frac{sin ( u )}{1 - 2 n} d u

Take the constant out:

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

= \frac{1}{1 - 2 n} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{1 - 2 n} (- cos (u))

Substitute back

u = x - 2 n x

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

Simplify

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

Add a constant to the solution

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

\frac{d}{d x} (x^{5} y^{2})

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

\int_{0}^{4} \frac{1}{( 6 - 2 x ) ^{\frac{1}{3}}} d x

(\frac{y ^{^{'}} - e ^{- t} + 5}{y}) = - 5, y (0) = - 2

\int \frac{5}{9 - ( x - 3 ) ^{2}} d x

What is the integral of sin(x-2nx) ?
The integral of sin(x-2nx) is -1/(1-2n)cos(x-2nx)+C