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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 4cos(2t)

\int 4 cos (2 t) d t

2 sin (2 t) + C

Solution steps

\int 4 cos (2 t) d t

Take the constant out:

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

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

Apply u-substitution

: \int cos (u) \frac{1}{2} d u

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = 2 t

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

Simplify

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

= 2 sin (2 t)

Add a constant to the solution

= 2 sin (2 t) + C

\int 4^{x} e^{x} d x

\int 24 x^{5} arctan (2 x^{3}) d x

\int e^{5 t} d t

\int \frac{cos ( x )}{sin ( x ) + 2} d x

\int 3^{x} sin (3^{x}) d x