What is the integral of 3cos(5θ) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3cos(5θ)

\int 3 cos (5 θ) d θ

\frac{3}{5} sin (5 θ) + C

Solution steps

\int 3 cos (5 θ) d θ

Take the constant out:

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

= 3 \cdot \int cos (5 θ) d θ

Apply u-substitution

: \int cos (u) \frac{1}{5} d u

= 3 \cdot \int cos (u) \frac{1}{5} d u

Take the constant out:

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

= 3 \cdot \frac{1}{5} \cdot \int cos (u) d u

Use the common integral:

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

= 3 \cdot \frac{1}{5} sin (u)

Substitute back

u = 5 θ

= 3 \cdot \frac{1}{5} sin (5 θ)

Simplify

3 \cdot \frac{1}{5} sin (5 θ) : \frac{3}{5} sin (5 θ)

= \frac{3}{5} sin (5 θ)

Add a constant to the solution

= \frac{3}{5} sin (5 θ) + C

\int \frac{1}{( x ^{2} - 2 x + 4 )} d x

\int \frac{5}{1 - x ^{2}} d x

\int (x^{3} - \frac{3}{1 + x ^{2}}) d x

\int (e^{- 9 x}) d x

\int 6 cos^{4} (3 x) d x