What is the integral of 1+cos(4x) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1+cos(4x)

\int 1 + cos (4 x) d x

x + \frac{1}{4} sin (4 x) + C

Solution steps

\int 1 + cos (4 x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d x + \int cos (4 x) d x

\int 1 d x = x

\int cos (4 x) d x = \frac{1}{4} sin (4 x)

= x + \frac{1}{4} sin (4 x)

Add a constant to the solution

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

5 x^{3} + 4 x

\int_{0}^{\infty} \frac{1}{x ^{2} + x} d x

\frac{\partial}{\partial y} (\frac{1}{x ^{2} + y ^{2} + 1})

\frac{d y}{d x} = - 0.05 y

\frac{\partial}{\partial y} (2 x y^{4} - 4)

What is the integral of 1+cos(4x) ?
The integral of 1+cos(4x) is x+1/4 sin(4x)+C