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

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

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integral of (sin(sqrt(w)))/(sqrt(w))

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

- 2 cos (w) + C

Solution steps

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

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 = w

= 2 (- cos (w))

Simplify

= - 2 cos (w)

Add a constant to the solution

= - 2 cos (w) + C

f (x) = x - 5, at x = 9

\frac{d}{d x} (3 8 x^{2})

(x^{2} + 5)^{5}

\int \frac{19}{19 + e ^{x}} d x

\frac{d}{d x} (\frac{1}{3 ^{- x^{2} - y^{2}} + 1})

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