What is the integral of sin((3x)/5) ?

The integral of sin((3x)/5) is -5/3 cos((3x)/5)+C

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integral of sin((3x)/5)

\int sin (\frac{3 x}{5}) d x

- \frac{5}{3} cos (\frac{3 x}{5}) + C

Solution steps

\int sin (\frac{3 x}{5}) d x

Apply u-substitution

= \int sin (u) \frac{5}{3} d u

Take the constant out:

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

= \frac{5}{3} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{5}{3} (- cos (u))

Substitute back

u = \frac{3 x}{5}

= \frac{5}{3} (- cos (\frac{3 x}{5}))

Simplify

= - \frac{5}{3} cos (\frac{3 x}{5})

Add a constant to the solution

= - \frac{5}{3} cos (\frac{3 x}{5}) + C

What is the integral of sin((3x)/5) ?
The integral of sin((3x)/5) is -5/3 cos((3x)/5)+C