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sat_chen
 one year ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=integral+of+%281%2F%28x%5E3*sqrt%28x%5E225%29%29%29dx

sat_chen
 one year ago
Best ResponseYou've already chosen the best response.0so what i am confused is on how someone went from

sat_chen
 one year ago
Best ResponseYou've already chosen the best response.0dw:1359567855994:dw

sat_chen
 one year ago
Best ResponseYou've already chosen the best response.0i think you have to log in to wolfram before you can see the steps

sat_chen
 one year ago
Best ResponseYou've already chosen the best response.0we get sin taking the integral of cos?

shubhamsrg
 one year ago
Best ResponseYou've already chosen the best response.0Yes I can't see the steps.

shubhamsrg
 one year ago
Best ResponseYou've already chosen the best response.0Was the substitution x = 5 siny ?

sat_chen
 one year ago
Best ResponseYou've already chosen the best response.0yea you have to log in for that i think and it would take me a year to type the solutions here XD

sat_chen
 one year ago
Best ResponseYou've already chosen the best response.0so someone with wolfram account tell me how they went from that step to the solution

shubhamsrg
 one year ago
Best ResponseYou've already chosen the best response.0Leme try anyways, let x= 5secy => dx= 5 secy tany dy so we have inside integral 5 secy tany dy/( 125 sec^3 y ( 25 + 25sec^2 y)^1/2) => 5sec y tany dy/( 625 sec^3 y (tan^2 y)^1/2 ) => 1/125 ( dy/sec^2y)) or simply cos^2y dy Am I right so far ?

sat_chen
 one year ago
Best ResponseYou've already chosen the best response.0i got a better way for you to see the solutions this is part 2 of the solution

sat_chen
 one year ago
Best ResponseYou've already chosen the best response.0theres all the steps to the solution can you take me from that 0/250 + sin20/500 + c to the solution

sat_chen
 one year ago
Best ResponseYou've already chosen the best response.0and yes you are right with your steps

sat_chen
 one year ago
Best ResponseYou've already chosen the best response.0so from the integral of (1/125)(cos^20d0) you do the half angle formula to get integral of (1/125)(1+cos20)/2dp then you split and get 0/250 + sin2(theta)/500 + c so my question if how you get from here to the answer

sat_chen
 one year ago
Best ResponseYou've already chosen the best response.0dw:1359570048133:dw

sat_chen
 one year ago
Best ResponseYou've already chosen the best response.0i get the second part where it is the inverse of sec1 (x/5) but i dont get where they got the 5sqrt(x^2) stuff from

sat_chen
 one year ago
Best ResponseYou've already chosen the best response.0dw:1359570931896:dw the stuff i dont get is in that box in case you are still confused on what i am confused about

phi
 one year ago
Best ResponseYou've already chosen the best response.0you are asking about \[ \frac{1}{2} \sin(2 u)\] with \[ u= \sec^{1}\left(\frac{x}{5}\right) \] In terms of cosine, rather than secant, we can say \[ u= \cos^{1}\left(\frac{5}{x}\right) \] If we take the hypotenuse to be x, in a triangle with side 5 dw:1359572361980:dw the other side is \( \sqrt{x^225} \) Using these sides, we have \[ \cos u = \frac{5}{x} \] and \[ \sin u = \frac{\sqrt{x^225}}{x} \] sin(2u) = 2 sin(u) cos(u) sub in the above definitions wolfram then multiplied by sqrt(x^2)/x (why?) to get your boxed expression
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