Question

"First make a substitution, then use integration by parts to evaluate the integral of 6sin(sqrt(x))dx." The only thing I can think of to sub is the sqrt(x) but then my dx is weird and I don't know where to go... help please?

Answer 1

here is my guess, but i hate these
\[u=\sqrt{x}\]
\[du=\frac{dx}{2\sqrt{x}}\]
\[2\sqrt{x}du=dx\]\[2udu=dx\]

Answer 2

then integrate
\[12\int u\sin(u)du\] by parts

Answer 3

oh right you can sub the u back in for the sqrt(x), i remember doing it in class now, thank you so much

Answer 4

the hint was "parts" otherwise i am sure i would not have guessed without it

Answer 5

since \(x\sin(x)\) is a set up for parts
yw