What is the integral of 3sin(3x+2) ?

The integral of 3sin(3x+2) is -cos(3x+2)+C

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integral of 3sin(3x+2)

\int 3 sin (3 x + 2) d x

- cos (3 x + 2) + C

Solution steps

\int 3 sin (3 x + 2) d x

Take the constant out:

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

= 3 \cdot \int sin (3 x + 2) d x

Apply u-substitution

: \int sin (u) \frac{1}{3} d u

= 3 \cdot \int sin (u) \frac{1}{3} d u

Take the constant out:

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

= 3 \cdot \frac{1}{3} \cdot \int sin (u) d u

Use the common integral:

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

= 3 \cdot \frac{1}{3} (- cos (u))

Substitute back

u = 3 x + 2

= 3 \cdot \frac{1}{3} (- cos (3 x + 2))

Simplify

3 \cdot \frac{1}{3} (- cos (3 x + 2)) : - cos (3 x + 2)

= - cos (3 x + 2)

Add a constant to the solution

= - cos (3 x + 2) + C

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