What is the integral of cos(x-nx) ?

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

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integral of cos(x-nx)

\int cos (x - n x) d x

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

Solution steps

\int cos (x - n x) d x

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = x - n x

= \frac{1}{1 - n} sin (x - n x)

Add a constant to the solution

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

\int e^{- x} x^{3} d x

y^{^{''}} + 4 y^{^{'}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = 13

9 (5^{x})

y^{^{'}} = 9 x y

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

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