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

\frac{d y}{d t} = y sin (t)

\int \frac{5 + u}{u} d u

\int_{- 2}^{2} \frac{1}{x ^{2} - 1} d x

\int \frac{18}{x} d x

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