Having trouble with substitution and integrals. The problem is evaluate the integral using an appropriate substition (sec^2)xdx/(sqrt(1-(tanx^2) s) i made u = ((sec^2)x) which seems to start the problem off ok but then I get lost towards the end. any help with steps would be greatly appreciated

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Anonymous Sun Jul 22 17:32:16 2012 No.4894689 [Reply] [Original]

Having trouble with substitution and integrals.

The problem is

evaluate the integral using an appropriate substition

(sec^2)xdx/(sqrt(1-(tanx^2) s)

i made u = ((sec^2)x) which seems to start the problem off ok but then I get lost towards the end.

any help with steps would be greatly appreciated

solution Anonymous Sun Jul 22 18:46:15 2012 No.4894847

ok! its easier than it looks at first sight:
the derivative of the tangent is 1/(cosx)²=(secx)²
so knowing this fact, if we take the change of variable M=Tanx the integral will be just the integral of the arcsinM
so the result is ArcSin(Tanx)+D

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