What is the integral of (8sin(sqrt(x)))/(sqrt(x)) ?

The integral of (8sin(sqrt(x)))/(sqrt(x)) is -16cos(sqrt(x))+C

Popular >

integral of (8sin(sqrt(x)))/(sqrt(x))

\int \frac{8 sin ( x )}{x} d x

- 16 cos (x) + C

Solution steps

\int \frac{8 sin ( x )}{x} d x

Take the constant out:

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

= 8 \cdot \int \frac{sin ( x )}{x} d x

Apply u-substitution

: \int 2 sin (u) d u

= 8 \cdot \int 2 sin (u) d u

Take the constant out:

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

= 8 \cdot 2 \cdot \int sin (u) d u

Use the common integral:

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

= 8 \cdot 2 (- cos (u))

Substitute back

u = x

= 8 \cdot 2 (- cos (x))

Simplify

= - 16 cos (x)

Add a constant to the solution

= - 16 cos (x) + C

\int \frac{x ^{5} - 1}{x ^{4} - 1} d x

\int (x - x)^{2} d x

\int (x^{2} + x + 1) e^{3 x} d x

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

\int x^{5} - 3 x + \frac{2}{x} d x

What is the integral of (8sin(sqrt(x)))/(sqrt(x)) ?
The integral of (8sin(sqrt(x)))/(sqrt(x)) is -16cos(sqrt(x))+C