Question

Integration sin^6(theta)cos^5(theta) dtheta

Answer 1

\[\int\limits_{}^{}\sin^6(\theta)\cos^5(\theta) d \theta\]

Answer 2

If I am not wrong, I think first I should change sin^6(theta) to (sin^2(theta))^3 ?

Answer 3

try changing cos^5 to cos^4 * cos = (1-sin^2)^2 * cos

Answer 4

so now I should use u = sin correct?

Answer 5

yes that will do

Answer 6

I got \[1/11\sin^11(\theta)-2/9\sin^9(\theta)+1/7\sin^7(\theta)+C\]

Answer 7

1/11 (sin(theta))^11 - 2/9 (sin(theta))^9 +1/7 (sin(theta))^7 +C

Answer 8

wolfram may not be useful here
http://www.wolframalpha.com/input/?i=%5Cint+%5Csin%5E6%28%5Ctheta%29%5Ccos%5E5%28%5Ctheta%29+d+%5Ctheta

Answer 9

it is simplifying too much

Answer 10

yeah, after I substitute. I had u^6 (1-u^2)^2

Answer 11

then u^6 (u^4 -2u^2 +1) after foil

Answer 12

then u^10 -2u^8 +u^6

Answer 13

ahh that looks trivial, no need to verify with wolfram ;)

Answer 14

then antideriving it would be 1/11 u^11 - 2/9 u^9 + 1/7 u^7 +C

Answer 15

yeah wolfram always does that with trigs :[

Answer 16

just a dumb tool >.>