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What is the solution of ​​∫sin³x.dx Should i put t=cosx³ and then solve it

What is the solution of  ​​∫sin³x.dx 
Should i put t=cosx³ and then solve it

Grade:12

1 Answers

Arun
25750 Points
4 years ago
Assuming you don't want to use the reduction formula . . . . . 

∫ sin³x dx = ∫sinx(1 – cos²x) dx 

u = cosx 
du/dx = - sinx 
- du = sinx dx 

- ∫ (1 – u²) du = 

- ∫du + ∫u² du = 

-u + (u³/3) + C = 

-cosx + (cos³x)/3 + C =  

C – cosx + (cos³x)/3 = 

and this can be simplified by factoring cosx and using identities 

C + [ (cos(3x) – 9cos(x)) / 12 ]

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