What is the integral of 9sin(3x) ?

The integral of 9sin(3x) is -3cos(3x)+C

Popular >

integral of 9sin(3x)

\int 9 sin (3 x) d x

- 3 cos (3 x) + C

Solution steps

\int 9 sin (3 x) d x

Take the constant out:

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

= 9 \cdot \int sin (3 x) d x

Apply u-substitution

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

= 9 \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

= 9 \cdot \frac{1}{3} \cdot \int sin (u) d u

Use the common integral:

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

= 9 \cdot \frac{1}{3} (- cos (u))

Substitute back

u = 3 x

= 9 \cdot \frac{1}{3} (- cos (3 x))

Simplify

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

= - 3 cos (3 x)

Add a constant to the solution

= - 3 cos (3 x) + C

x \to - 2 lim (x^{2} - 4)

f (x) = x^{\frac{4}{3}}

\int_{2 π}^{\infty} sin (x) d x

\int_{1}^{e} ln (18 x) d x

y = (x + 1) 1 - 2 x