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appleduardo
 2 years ago
whats the integral of sin x^(3) 3x^(2)?
appleduardo
 2 years ago
whats the integral of sin x^(3) 3x^(2)?

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NicoleLe
 2 years ago
Best ResponseYou've already chosen the best response.01/36 (81 (x^22) cos(x)+(9 x^22) cos(3 x)6 x (sin(3 x)27 sin(x)))+C

appleduardo
 2 years ago
Best ResponseYou've already chosen the best response.0i know i have to use u du = cos u +c, but dont know how to do it step by step :/

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0LEt x^3 = u see if it works ?

appleduardo
 2 years ago
Best ResponseYou've already chosen the best response.0cos(x)^(3) + C is that correct?

appleduardo
 2 years ago
Best ResponseYou've already chosen the best response.0but what happened with du (which equals to 3x^2 ) ?

NicoleLe
 2 years ago
Best ResponseYou've already chosen the best response.0make the function as 3x^2* sinx^3

NicoleLe
 2 years ago
Best ResponseYou've already chosen the best response.0do u know trig identities of sin^2 X??

NicoleLe
 2 years ago
Best ResponseYou've already chosen the best response.0separate sin^3x into Sin^2x Sinx

NicoleLe
 2 years ago
Best ResponseYou've already chosen the best response.0its now become 3Integral X^2(sinX)(1/2(1cos2x)dx

NicoleLe
 2 years ago
Best ResponseYou've already chosen the best response.0convert that into 3/2 int x^2(sinx)(1cos2x)dx

NicoleLe
 2 years ago
Best ResponseYou've already chosen the best response.0Use the trigonometric identity sin(a) cos(b) 3/2 integral x^2 sin(x)dx  3/4 integral x^2 (sin(3 x)sin(x)) dx

NicoleLe
 2 years ago
Best ResponseYou've already chosen the best response.0its become 3/2 integral x^2 sin(x) dx  3/4integral (x^2 sin(3 x)x^2 sin(x)) dx

NicoleLe
 2 years ago
Best ResponseYou've already chosen the best response.0Integrate the sum term by term and factor out constants: = 3/4 integral x^2 sin(x) dx3/4 integral x^2 sin(3 x) dx+3/2 integral x^2 sin(x) dx

NicoleLe
 2 years ago
Best ResponseYou've already chosen the best response.0im just gonna write it out what i do next.. just copy in out then u'll see

NicoleLe
 2 years ago
Best ResponseYou've already chosen the best response.01/4 x^2 cos(3 x)+3/2 integral x^2 sin(x) dx+3/4 integral x^2 sin(x) dx1/2 integral x cos(3 x) dx

NicoleLe
 2 years ago
Best ResponseYou've already chosen the best response.0= 1/4 x^2 cos(3 x)+3/2 integral x^2 sin(x) dx+3/4 integral x^2 sin(x) dx1/6 x sin(3 x)+1/6 integral sin(3 x) dx

NicoleLe
 2 years ago
Best ResponseYou've already chosen the best response.0= 1/18 integral sin(u) du+1/4 x^2 cos(3 x)+3/2 integral x^2 sin(x) dx+3/4 integral x^2 sin(x) dx1/6 x sin(3 x)

NicoleLe
 2 years ago
Best ResponseYou've already chosen the best response.01/18 integral sin(u) du3/4 x^2 cos(x)+1/4 x^2 cos(3 x)+3/2 integral x^2 sin(x) dx1/6 x sin(3 x)+3/2 integral x cos(x) dx

NicoleLe
 2 years ago
Best ResponseYou've already chosen the best response.01/18 integral sin(u) du3/4 x^2 cos(x)+1/4 x^2 cos(3 x)+3/2 integral x^2 sin(x) dx+3/2 x sin(x)1/6 x sin(3 x)3/2 integral sin(x) dx

NicoleLe
 2 years ago
Best ResponseYou've already chosen the best response.0= (cos(u))/181/4 (3 x^2 cos(x))+1/4 x^2 cos(3 x)+3/2 integral x^2 sin(x) dx+3/2 x sin(x)1/6 x sin(3 x)3/2 integral sin(x) dx = (cos(u))/183/4 x^2 cos(x)+1/4 x^2 cos(3 x)+3/2 integral x^2 sin(x) dx+3/2 x sin(x)1/6 x sin(3 x)+(3 cos(x))/2 = (cos(u))/189/4 x^2 cos(x)+1/4 x^2 cos(3 x)+3/2 x sin(x)1/6 x sin(3 x)+(3 cos(x))/2+3 integral x cos(x) dx = (cos(u))/189/4 x^2 cos(x)+1/4 x^2 cos(3 x)+9/2 x sin(x)1/6 x sin(3 x)+(3 cos(x))/23 integral sin(x) dx The integral of sin(x) is cos(x): = (cos(u))/189/4 x^2 cos(x)+1/4 x^2 cos(3 x)+9/2 x sin(x)1/6 x sin(3 x)+(9 cos(x))/2+constant Substitute back for u = 3 x: = 9/4 x^2 cos(x)+1/4 x^2 cos(3 x)+9/2 x sin(x)1/6 x sin(3 x)+(9 cos(x))/21/18 cos(3 x)+constant Which is equal to: Answer:   = 1/36 (81 (x^22) cos(x)+(9 x^22) cos(3 x)6 x (sin(3 x)27 sin(x)))+constant

NicoleLe
 2 years ago
Best ResponseYou've already chosen the best response.0I happen to did this before so im pretty sure its right .. but good luck,, check it w ur teacher , but if it wrong then please dont kill me ^^

appleduardo
 2 years ago
Best ResponseYou've already chosen the best response.0oh my gosh! what a long integral! thank you so much for help me out!, and be sure i wont kill u if its wrong :P :D ^^

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0hmm, I did not read what you wrote but certainly no need for all that. after letting x^3 = u, => 3x^2 dx= du so integral becomes (sin u du) => cos u + C =>cos(x^3) + C as simple as that.
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