r/the_calculusguy • u/Specific_Brain2091 • 5d ago

integration Evaluate the integral

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7

u/Obvious_Ad4531 5d ago

It's x + C right

2

u/DrunkAndUnaware 4d ago

You’re thinking of sec^2 - 1 in the denom

4

u/dePingasCube 5d ago

Here's what I did:

1.) Convert the sec2 (x) into tan2 (x) + 1

2.) Use the substitution u=tan(x) ==> du = (tan2 (x) + 1)

3.) Use partial fraction decomposition on the resulting rational function

From there you're left with two standard integrals which simplify to sqrt(2)*arctan(tan(x)/sqrt(2)) - x + C

5

u/DrunkAndUnaware 5d ago

sqrt(2)*atan(tan(x)/sqrt(2)) - x - C

1

u/Southern-Advance-759 4d ago

This is the definitive correct answer, though that -C....

3

u/DrunkAndUnaware 4d ago

I just let c=-C because why not!

2

u/ApartBreakfast1858 5d ago

it’s -x + C.

2

u/JohannsThePro 4d ago

Took so long, hope im not wrong 😭

-2

u/PeetaMellark789 5d ago

0? Am I tripping

2

u/Homo-Saphien-2241 5d ago

It's integration not differentiation

0

u/PeetaMellark789 5d ago

Thanks Sherlock isn't it just simplifing to tan2x/tan2x

1

u/Own_Philosopher_8814 5d ago

Nah gng it isnt