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

\frac{( s - 2 )}{( s - 2 ) ^{2} - 3}

\int \frac{( e ^{x} )}{1 + e ^{x}} d x

y = 4 t t + 7

\int_{- 2}^{2} x^{2} - 1 d x

f (x) = 2 e^{- x}

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