Question

The integral of xarccos(x)dx
It's supposed to be solved using a table of integrals...however, my prof. wants us to solve all our HW probs NOT using a table of integrals.
Any help is appreciated, even any hints about how to go about solving w/o integral table would be great! Thanks

Answer 1

by parts

Answer 2

u = cos^-1(x)
dv = x dx

Answer 3

du = -1/ sqrt(1-x^2) dx

v = (1/2)x^2

Answer 4

Thanks! I was leaning towards parts, but was second guessing.

Answer 5

it should be easy

Answer 6

v du is just an algebraic function

Answer 7

easy to integrate

Answer 8

wait

Answer 9

Cool. I'll give it a shot

Answer 10

u need trig sub

Answer 11

instead of parts altogether? Or in addition to?

Answer 12

no u need parts

Answer 13

then integration by parts says its

uv - integral v du

Answer 14

v du is something like x^2 / sqrt(1-x^2) with some constant floating around

Answer 15

Oh i see where it's going to need trig substitution

Answer 16

that integral needs a trig substitution

Answer 17

cool cool, yea that makes sense