How to find the integal of

Determine:
π2/4
∫ [((cos.sqrt(x))/ sqrt (x) ] dx
0

∫cos(√x))/√x dx from 0 to π²/4

u = √x

2 du = dx/√x

2*∫cos(u) du eval. from 0 to π/2

2*sin(u) eval. from 0 to π/2

= 2

u substitution

u = sqrt(x)
du = dx / (2 * sqrt(x))

Now we have:

2 * cos(u) * du

Integrate

2 * sin(u) + C

Back-substitute

2 * sin(sqrt(x)) + C

From 0 to pi^2 / 4

2 * sin(sqrt(pi^2 / 4)) - 2 * sin(sqrt(0)) =>
2 * sin(pi/2) - 2 * sin(0) =>
2 * 1 - 2 * 0 =>
2 - 0 =>
2