What is the integral of 4cos(sqrt(4x)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 4cos(sqrt(4x))

\int 4 cos (4 x) d x

2 (2 x sin (2 x) + cos (2 x)) + C

Solution steps

\int 4 cos (4 x) d x

Take the constant out:

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

= 4 \cdot \int cos (4 x) d x

Apply u-substitution

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

= 4 \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

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

Apply u-substitution

: \int cos (v) \cdot 2 v d v

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

Take the constant out:

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

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

Apply Integration By Parts

: v sin (v) - \int sin (v) d v

= 4 \cdot \frac{1}{4} \cdot 2 (v sin (v) - \int sin (v) d v)

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

= 4 \cdot \frac{1}{4} \cdot 2 (v sin (v) - (- cos (v)))

Substitute back

= 4 \cdot \frac{1}{4} \cdot 2 (4 x sin (4 x) - (- cos (4 x)))

Simplify

4 \cdot \frac{1}{4} \cdot 2 (4 x sin (4 x) - (- cos (4 x))) : 2 (2 x sin (2 x) + cos (2 x))

= 2 (2 x sin (2 x) + cos (2 x))

Add a constant to the solution

= 2 (2 x sin (2 x) + cos (2 x)) + C

x \to 1 + lim ((x - 1)^{(x - 1)})

\frac{4 - 2 x - x ^{2}}{x ^{2} - 6}

B (x - 2)^{3}

\frac{\partial}{\partial x} (x sin (x) e^{y x^{2}})

(6, - 1), (3, - 7)

What is the integral of 4cos(sqrt(4x)) ?
The integral of 4cos(sqrt(4x)) is 2(2sqrt(x)sin(2sqrt(x))+cos(2sqrt(x)))+C