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

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

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

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

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

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

imperialist
 3 years ago
Best ResponseYou've already chosen the best response.0You will be pleasantly surprised!

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

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

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

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