What is the integral of sin(inx) ?

The integral of sin(inx) is -1/(in)cos(inx)+C

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integral of sin(inx)

\int sin (in x) d x

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

Solution steps

\int sin (in x) d x

Apply u-substitution

: \int \frac{sin ( u )}{in} d u

= \int \frac{sin ( u )}{in} d u

Take the constant out:

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

= \frac{1}{in} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{in} (- cos (u))

Substitute back

u = in x

= \frac{1}{in} (- cos (in x))

Simplify

= - \frac{1}{in} cos (in x)

Add a constant to the solution

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

\int_{- 1}^{0} 1

\int e^{\frac{x}{y}} d x

x \to 0 - lim (\frac{8}{x} - \frac{8}{∣ x ∣})

\int \frac{x - 2 x ^{2}}{x} d x

\int arccos (y) d y

What is the integral of sin(inx) ?
The integral of sin(inx) is -1/(in)cos(inx)+C