What is the integral of (sin(x^{1/2}))/(x^{1/2)} ?

The integral of (sin(x^{1/2}))/(x^{1/2)} is -2cos(x^{1/2})+C

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integral of (sin(x^{1/2}))/(x^{1/2)}

\int \frac{sin ( x ^{\frac{1}{2}} )}{x ^{\frac{1}{2}}} d x

- 2 cos (x^{\frac{1}{2}}) + C

Solution steps

\int \frac{sin ( x ^{\frac{1}{2}} )}{x ^{\frac{1}{2}}} d x

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 = x^{\frac{1}{2}}

= 2 (- cos (x^{\frac{1}{2}}))

Simplify

= - 2 cos (x^{\frac{1}{2}})

Add a constant to the solution

= - 2 cos (x^{\frac{1}{2}}) + C

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What is the integral of (sin(x^{1/2}))/(x^{1/2)} ?
The integral of (sin(x^{1/2}))/(x^{1/2)} is -2cos(x^{1/2})+C