Need to check an integral answer.
integral sin^5(x) * cos^4(x) dx

Question

Need to check an integral answer.
integral sin^5(x) * cos^4(x) dx

anonymous · Answer

I said u = cos(x)
so du/-sin(x) = dx

anonymous · Answer

so now I have...

anonymous · Answer

$$\int\limits (1-\cos^2(x))(1-\cos^2(x))(\cos^4(x))(\sin(x)$$ dx

anonymous · Answer

after substitution I have ...

anonymous · Answer

$$\int\limits (1-u^2)(1-u^2)(u^4)(\sin(x))du/-\sin(x)$$

anonymous · Answer

which should simplify to...

anonymous · Answer

$$\int\limits u^8 - 2u^6 + u^4 du$$

anonymous · Answer

final answer (-1/9)cos^9(x) + (2/7)cos^7(x) + (1/5)cos^5(x) + C

anonymous · Answer

What do you think John?

johnweldon1993 · Answer

Doing it out on paper, hang on 1 sec

anonymous · Answer

Thank you.

johnweldon1993 · Answer

Ehh by parts is terrible...let me try a reduction instead sorry for the wait @jasonjohnson86

anonymous · Answer

It should just be either a sin or cos sub (; Thats what Im working out of in my book.

anonymous · Answer

With the power reduction.

johnweldon1993 · Answer

Yeah I thought somewhere along the way something got left behind...just trying to figure out where... And I just check wolfram just to double check http://www.wolframalpha.com/input/?i=integral+%28sin%5E5%28x%29cos%5E4%28x%29dx%29

anonymous · Answer

Yeah already checked that, don''t like the form of it. I think I should be able to get an answer this route.

anonymous · Answer

Yeah this should be good.....unless anyone has any issues with what I did. I dropped a negative sign on one term. should be (-1/5)cos^5(x)

anonymous · Answer

solution should be (-1/9)cos^9(x) + (2/7)cos^7(x) + (-1/5)cos^5(x)

primeralph · Answer

|dw:1397267453397:dw|