Question

we are starting trig subs...how do you solve integral4sin^7xcos^7xdx?

Answer 1

you want to find the following \[\int\limits_{}^{}(4*\sin(x*\cos(x)^7)^7)dx\] ?

Answer 2

integral of (4)(sin^7x)(cos^7x) dx

Answer 3

replace sin^7x by
sin(x)(sin^2x)^3
sin(x) (1-cos^2(x))^3

can you do it now ?

Answer 4

your integral will become :
4sin(x)cos^7(x)(1-cos^2(x))^3
4sin(x)cos^7(x)(1-3cos^2(x)+3cos^4(x)-cos^6(x))
and this is an easy one (-sin(x) is the derivative of cos(x)..)

Answer 5

are you there ?

Answer 6

did i write it correctly..in that the x after the 7s are not in the power area...so it should read ^7(x) not ^7x

Answer 7

yes

Answer 8

\[4\cos(7x)\sin(7x)\]

Answer 9

?

Answer 10

\[4\cos^7(x)\sin^7(x)\]

Answer 11

first or second ? which one of them

Answer 12

yes on second with a dx

Answer 13

so i answered you for the second one .. it is in the power area..

Answer 14

=\[4\sin(x)(\sin^2(x))^3 \cos^7(x)\]
=\[4\cos^7(x)\sin(x)(1-\cos^2(x))^3\]
= \[4\cos^7(x)\sin(x)(1-3\cos^2(x)+3\cos^4(x)-\cos^6(x))\]

Answer 15

you should be able to integrate it right now

Answer 16

ok, since i wasnt sure i wanted to make sure i presented it correctly, is the above answer including the steps to solve the problem? sorry, 1st time on here not sure how to do this

Answer 17

i just showed you i got to the last line ..
now you have to integrate it

Answer 18

great i will take it from there and try...thanks so much...much appreciated

Answer 19

yw