What is the integral of 3cos(sqrt(x)) ?

The integral of 3cos(sqrt(x)) is 6(sqrt(x)sin(sqrt(x))+cos(sqrt(x)))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3cos(sqrt(x))

\int 3 cos (x) d x

6 (x sin (x) + cos (x)) + C

Solution steps

\int 3 cos (x) d x

Take the constant out:

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

= 3 \cdot \int cos (x) d x

Apply u-substitution

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

= 3 \cdot \int cos (u) \cdot 2 u d u

Take the constant out:

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

= 3 \cdot 2 \cdot \int cos (u) u d u

Apply Integration By Parts

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

= 3 \cdot 2 (u sin (u) - \int sin (u) d u)

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

= 3 \cdot 2 (u sin (u) - (- cos (u)))

Substitute back

u = x

= 3 \cdot 2 (x sin (x) - (- cos (x)))

Simplify

= 6 (x sin (x) + cos (x))

Add a constant to the solution

= 6 (x sin (x) + cos (x)) + C

\frac{d}{d x} (x^{2} + k)

\int (10 x - 9) d x

3 y^{^{'}} + 12 y = 24

\frac{\partial}{\partial y} (6 x + 6 y)

\int (x^{3} - 7 x)^{4} (3 x^{2} - 7) d x

What is the integral of 3cos(sqrt(x)) ?
The integral of 3cos(sqrt(x)) is 6(sqrt(x)sin(sqrt(x))+cos(sqrt(x)))+C