What is the integral of 2cos(4t) ?

The integral of 2cos(4t) is 1/2 sin(4t)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2cos(4t)

\int 2 cos (4 t) d t

\frac{1}{2} sin (4 t) + C

Solution steps

\int 2 cos (4 t) d t

Take the constant out:

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

= 2 \cdot \int cos (4 t) d t

Apply u-substitution

: \int cos (u) \frac{1}{4} d u

= 2 \cdot \int cos (u) \frac{1}{4} d u

Take the constant out:

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

= 2 \cdot \frac{1}{4} \cdot \int cos (u) d u

Use the common integral:

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

= 2 \cdot \frac{1}{4} sin (u)

Substitute back

u = 4 t

= 2 \cdot \frac{1}{4} sin (4 t)

Simplify

2 \cdot \frac{1}{4} sin (4 t) : \frac{1}{2} sin (4 t)

= \frac{1}{2} sin (4 t)

Add a constant to the solution

= \frac{1}{2} sin (4 t) + C

\int cot^{- 3} (3 y) csc^{4} (3 y) d y

\int 12 x - 12 x^{3} d x

\int (x + 1)^{10} (x + 5) d x

\int \frac{2 x}{e ^{- x}} d x

\int \frac{x + 10}{x ^{2} + 3 x + 2} d x