Can someone please help me to evaluate these integrals
ò sin ^5 x dx
ò tan 3 x dx
Do I simply apply rule one for adding the the exponent and placing the same exponent in the denominator? Do I substitue -cos for sin? Do I substitute sec^2 x for tan x? Help please.
I'm not sure what you mean by "adding the exponent". If you were thinking of the power rule, no, because this is , you cannot do that.
Because of the odd power in , you can factor out one "sin t" to use with the derivative: . Now use the substitution u= cos x, du= -sin x dx so the integral becomes . Multiply that out and you can apply the power rule to each part.
For you can't "substitute sec^2 x for tan x"- they are not equal! It is the derivative of tan x that is equal to and you don't have any derivative of tan x in this. I would write it in the form . Again, that is an odd power of sine so we can factor out one to use with dx:
. Again, let u= cos(x) so that du= -sin x dx so the integral becomes .
Thank you. I am struggling trying to lean Calculus. I was on the wrong track (confused). I now have a better understanding of the substitution fule, usign u= cosx. I will keep trying. I guess I am just not that smart. I have to leanr to ask questions sooner or somehow try to comprehend faster. I have a test in a couple of hours. Too bad for me that nobody seems to think it beneficial just to show me how to do the problems. But I truly thank you for putting me on the right track.