What is the integral of (4sin((5x)/3))/(7) ?

The integral of (4sin((5x)/3))/(7) is -12/35 cos((5x)/3)+C

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integral of (4sin((5x)/3))/(7)

\int \frac{4 sin ( \frac{5 x}{3} )}{7} d x

- \frac{12}{35} cos (\frac{5 x}{3}) + C

Solution steps

\int \frac{4 sin ( \frac{5 x}{3} )}{7} d x

Take the constant out:

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

= \frac{4}{7} \cdot \int sin (\frac{5 x}{3}) d x

Apply u-substitution

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

= \frac{4}{7} \cdot \int sin (u) \frac{3}{5} d u

Take the constant out:

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

= \frac{4}{7} \cdot \frac{3}{5} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{4}{7} \cdot \frac{3}{5} (- cos (u))

Substitute back

u = \frac{5 x}{3}

= \frac{4}{7} \cdot \frac{3}{5} (- cos (\frac{5 x}{3}))

Simplify

\frac{4}{7} \cdot \frac{3}{5} (- cos (\frac{5 x}{3})) : - \frac{12}{35} cos (\frac{5 x}{3})

= - \frac{12}{35} cos (\frac{5 x}{3})

Add a constant to the solution

= - \frac{12}{35} cos (\frac{5 x}{3}) + C

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What is the integral of (4sin((5x)/3))/(7) ?
The integral of (4sin((5x)/3))/(7) is -12/35 cos((5x)/3)+C