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Popular >

integral of cos(sqrt(x)) 1/(sqrt(x))

Solution

\int cos (x) \frac{1}{x} d x

Solution

2 sin (x) + C

Solution steps

\int cos (x) \frac{1}{x} d x

Simplify

cos (x) \frac{1}{x} : \frac{cos ( x )}{x}

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

Apply u-substitution

: \int 2 cos (u) d u

= \int 2 cos (u) d u

Take the constant out:

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

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

Use the common integral:

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

= 2 sin (u)

Substitute back

u = x

= 2 sin (x)

Add a constant to the solution

= 2 sin (x) + C

Popular Examples

integral of x^2(3x^3-1)^4

\int x^{2} (3 x^{3} - 1)^{4} d x

integral of 4-2x^2

\int 4 - 2 x^{2} d x

integral of (x+3)/(x^2-2x+5)

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

integral of (2x^8-7x^4)/(3x^9)

\int \frac{2 x ^{8} - 7 x ^{4}}{3 x ^{9}} d x

integral of 2xe^y+(2x)/y+1/(y^3)

\int 2 x e^{y} + \frac{2 x}{y} + \frac{1}{y ^{3}} d x

Frequently Asked Questions (FAQ)

What is the integral of cos(sqrt(x)) 1/(sqrt(x)) ?
The integral of cos(sqrt(x)) 1/(sqrt(x)) is 2sin(sqrt(x))+C