Question

Indefinite Integral

\(\large{ \int \sin (2x) \cos (3x) dx }\)

Answer 1

2sinAcosB identity

Answer 2

\(\large{ \int 2\sin x \cos x \left[4 \cos^3 (x) - 3\cos (x) \right] }\)

Answer 3

this identity simplifies the work :
2sinAcosB = sin(A+B) + sin(A-B)

Answer 4

\(\large{ 2 \int \sin x \cos x (\cos x ) \left[ 4\cos^2 (x) - 3 \right] \\
2 \int \sin x \cos^2 x \left[ 4(1-\sin^2 x) -3 \right] }\)

Answer 5

\(\large{ 2 \int \sin x ( 1- \sin^2 x) \left[ 1 - 4\sin^2 x \right] }\)

Am I going on wrong track?

Answer 6

nope, you're in right track... but thats a lengthy procss

Answer 7

Yeah.. that seems to be lengthy. I tried a lot, though, I didn't get a feeling that I am on wrong track, but the answer I got doesn't match the correct answer.

Answer 8

try working it again using the angle sum formula

Answer 9

Using the angle sum formula here? Never did this before, can you give me a brief idea for this?

Answer 10

Okay, well, I think I got your point :

\(\int \sin (2x) \cos (3x) \)
\(\cfrac{1}{2} \int 2\sin (2x) \cos (3x) \)

Answer 11

\(\cfrac{1}{2} \int (\sin (5x) - \sin (x) )dx\)

Answer 12

Yep !

Answer 13

Okay, yeah, am getting that @ganeshie8 ...!

Answer 14

So, that becomes :

\(\cfrac{1}{2} \times \cfrac{-\cos^5 x}{5} - \cfrac{1}{2} \times (-\cos x) +C\)

Answer 15

Looks good !

Answer 16

oh wait a sec, bring that exponent back to its place lol

Answer 17

Got it...

\(\cfrac{-1}{10} (\cos 5 x) + \cfrac{1}{2} \cos x + C\)

Oh sorry lol

Answer 18

That 5 was so nasty... didn't want to live with x... so, he decided to become an exponent! I was helpless :P

Jokes apart, Thanks a lot @ganeshie8 .. You did it again. :)

Answer 19

oh hahaa

Answer 20

""The nasty5"" by @mathslover. First day first show at OS Talkies.


Hurry before the film becomes HOUSE FULL lol ;) :P

Answer 21

Ah... the ticket costs 1 billion dollars. Who wants to buy it?

Answer 22

For tickets in black contact @vishweshshrimali5. Hurry offer limited.

Answer 23

Well, it seems the people are not that interested in nasty5 we will have to work for the sequel. LOL

Answer 24

Flop show :( May be @ganeshie8 and @Miracrown want to buy the ticket? (0.1 % discount for them :P )

Answer 25

lol the talk in the town is that they're giving the tickets for free :P

Answer 26

nty, films don't interest me.

Answer 27

Well we also have the comic version of NASTY 5. Signed by superman and batman. @Miracrown
Interested ?
@mathslover is bearing the whole cost .

Answer 28

@ganeshie8 I started the rumour.

Answer 29

Ohh no, I spoiled the serious environment. Bye guys ;)

And yes great work @ganeshie8 and @mathslover

Answer 30

Someone just stole my piggy bank... It contained 1 billion dollars. Anyone interested to donate ? =P

Well, being an ambi, I am bound to abide with the rules... :( This has become off-topic, so we will continue this discussion when we get the answer in the next post.

Thanks @ganeshie8 and its okay @vishweshshrimali5 :-)
@Miracrown - You must have bought the ticket... :( It was really a nice movie.

Answer 31

I think she will join if the film is released in space theater :
http://www.virgingalactic.com/

:)

Answer 32

We will have to look into that. Don't worry we will try to turn up with a solution for that also.

Answer 33

A committee will be formed for this ... lol
Now, as @Miracrown is not buying the ticket, unfortunately, the show ENDS here. lol

Answer 34

uhm- I will never buy the tickets-no matter what!
even if it gets released in the space theater (which it never will, and its just virtual thinking... I will still not join. -.-