- #1

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My try:

Let dv = cos(√x) => v = 2√xsin(√x) and u = √x => du = dx/(2√x)

Using integration by parts, we get

∫√x cos(√x) dx = 2√x√x sin(√x) - ∫(2√xsin(√x) dx)/(2√x)

= 2x sin(√x) - ∫sin(√x) dx

= 2x sin(√x) + 2 cos(√x) √x

However, the answer given in the book is: http://www.wolframalpha.com/input/?i=integrate+sqrt(x)++cos(sqrt(x))

And a solution that I found says: http://www.slader.com/textbook/9780534465544-calculus-early-transcendentals/601/61-exercises/23/

Which one of us is correct? And if I am wrong, what am I doing wrong and how may I correct it?