What is the integral of (sin(sqrt(θ)))/(sqrt(θ)) ?

The integral of (sin(sqrt(θ)))/(sqrt(θ)) is -2cos(sqrt(θ))+C

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integral of (sin(sqrt(θ)))/(sqrt(θ))

\int \frac{sin ( θ )}{θ} d θ

- 2 cos (θ) + C

Solution steps

\int \frac{sin ( θ )}{θ} d θ

Apply u-substitution

: \int 2 sin (u) d u

= \int 2 sin (u) d u

Take the constant out:

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

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

Use the common integral:

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

= 2 (- cos (u))

Substitute back

u = θ

= 2 (- cos (θ))

Simplify

= - 2 cos (θ)

Add a constant to the solution

= - 2 cos (θ) + C

\int \frac{3 e ^{2 x}}{e ^{2 x} + 13 e ^{x} + 40} d x

x \to 0 lim (- x^{2} + 3 x + a)

\frac{d h}{d t} = 0.3 (5 - h)

\int 36 t (9 t^{2} - 7)^{3} d t

4 sin (2 t)

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