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

The integral of 4cos(sqrt(x)) is 8(sqrt(x)sin(sqrt(x))+cos(sqrt(x)))+C

Popular >

integral of 4cos(sqrt(x))

\int 4 cos (x) d x

8 (x sin (x) + cos (x)) + C

Solution steps

\int 4 cos (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 (x) d x

Apply u-substitution

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

= 4 \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

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

Apply Integration By Parts

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

= 4 \cdot 2 (u sin (u) - \int sin (u) d u)

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

= 4 \cdot 2 (u sin (u) - (- cos (u)))

Substitute back

u = x

= 4 \cdot 2 (x sin (x) - (- cos (x)))

Simplify

= 8 (x sin (x) + cos (x))

Add a constant to the solution

= 8 (x sin (x) + cos (x)) + C

f (x) = x^{\frac{3}{2}} + \frac{1}{x ^{\frac{5}{2}}}

\frac{d}{d x} (x^{2} e^{7 x})

\int \frac{( e ^{t} + 2 e ^{2 t} )}{e ^{3 t}} d t

\frac{\partial}{\partial x} (\frac{u}{x})

\int_{- 1}^{1} 2 1 - \frac{x ^{2}}{2} d x

What is the integral of 4cos(sqrt(x)) ?
The integral of 4cos(sqrt(x)) is 8(sqrt(x)sin(sqrt(x))+cos(sqrt(x)))+C