Question

Evaluate the integral:

Answer 1

\[\LARGE \int sin^2(\pi x)~cos^5(\pi x)~dx\]

Answer 2

assume cos(πx) =z and proceed further

Answer 3

\[\int sin^2(\pi x)~cos^5(\pi x)~dx = \int sin^2(\pi x)~\left(1-sin^2(\pi x)\right)^2 \cos (\pi x)~dx\]

Answer 4

sin(πx) =z will work..

Answer 5

\[\frac{ 1 }{ \pi }\int\limits \sin^2(u)\cos^5(u)du \]

u = pi*x , du = pi dx

\[\frac{ 1 }{ \pi } \int\limits \sin^2(u)(1-\sin^2(u))^2\cos(u)du\]

sin^2u = 1-cos^2u

\[\frac{ 1 }{ \pi } t^2(1-t^2)^2dt\]

t = sinu, dt = cosudu

etc, etc.

Answer 6

there should be a integral sign before t^2 lol

Answer 7

A good integration problem , although this isn't rocket science

Answer 8

\[\frac{ \sin ^{3}(\pi x) (15\cos ^{4}(\pi x ) + 12\cos ^{2}(\pi x)+8)}{ 105\pi } + C\]

Answer 9

This must be the answer

Answer 10

Is this the answer

Answer 11

Substitute u =pi x

dx =[1/pi] du

Henceforth it would be easy , You will need to apply integral substitution once more :)

Answer 12

THANK YOU MICHIO THANK YOU SO MUCH FOR YOUR COMMITMENT

Answer 13

And Apply integral reduction twice before that

Answer 14

Okay, thank you all :D

Answer 15

Nice integration problem !

Answer 16

Good luck!

Answer 17

>.< michio