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

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

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integral of (sin(sqrt(t)))/(sqrt(t))

\int \frac{sin ( t )}{t} d t

- 2 cos (t) + C

Solution steps

\int \frac{sin ( t )}{t} d t

Apply u-substitution

= \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 = t

= 2 (- cos (t))

Simplify

= - 2 cos (t)

Add a constant to the solution

= - 2 cos (t) + C

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