What is the integral of (cos(5sqrt(x)))/(sqrt(x)) ?

The integral of (cos(5sqrt(x)))/(sqrt(x)) is 2/5 sin(5sqrt(x))+C

Popular >

integral of (cos(5sqrt(x)))/(sqrt(x))

\int \frac{cos ( 5 x )}{x} d x

\frac{2}{5} sin (5 x) + C

Solution steps

\int \frac{cos ( 5 x )}{x} d x

Apply u-substitution

: \int \frac{2 cos ( u )}{5} d u

= \int \frac{2 cos ( u )}{5} d u

Take the constant out:

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

= \frac{2}{5} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{2}{5} sin (u)

Substitute back

u = 5 x

= \frac{2}{5} sin (5 x)

Add a constant to the solution

= \frac{2}{5} sin (5 x) + C

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

\int x arcsin (2 x) d x

\int \frac{1}{cos ^{2} ( x ) tan ( x ) - 1} d x

\int \frac{5 tan ( x ) - 2 cos ^{2} ( x )}{cos ( x )} d x

\int \frac{5 x ^{2} - 36 x + 48}{x ( x - 4 ) ^{2}} d x

What is the integral of (cos(5sqrt(x)))/(sqrt(x)) ?
The integral of (cos(5sqrt(x)))/(sqrt(x)) is 2/5 sin(5sqrt(x))+C