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Use the given trig identity to set up a usubstitution and then evaluate the indefinite integral.
 2 years ago
 2 years ago
Use the given trig identity to set up a usubstitution and then evaluate the indefinite integral.
 2 years ago
 2 years ago

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FoolForMathBest ResponseYou've already chosen the best response.3
Yes, where are you stuck?
 2 years ago

imperialistBest ResponseYou've already chosen the best response.0
Hint: what is the derivative of tan(x)?
 2 years ago

DenebelBest ResponseYou've already chosen the best response.1
How to start? Can I do this ? dw:1326790556349:dw
 2 years ago

DenebelBest ResponseYou've already chosen the best response.1
Derivative of tan x is (sec x)^2
 2 years ago

imperialistBest ResponseYou've already chosen the best response.0
Yes, so try only breaking one of the (sec x)^2 into 1+(tan x)^2
 2 years ago

imperialistBest ResponseYou've already chosen the best response.0
You will be pleasantly surprised!
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.3
\[ \int \sec^4 x \space dx = \int (1+\tan^2 x) \sec^2 x \space dx \]
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.3
Now put \( \tan x = z \implies \sec^2 x dx = dz \)
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.3
So, \[ \int (1+\tan^2 x) \sec^2 x \space dx = \int (1+z^2) dz \] I am sure you can proceed after this.
 2 years ago

DenebelBest ResponseYou've already chosen the best response.1
Oh I see now. Thank you very much!
 2 years ago
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