#Weird integration substitution question

17 messages · Page 1 of 1 (latest)

steel glen
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this is the question

20230124_145745.png
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this is the answer

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but when you differentiate that you wont get the function that you are integrating

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another one of my friends said its

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ln (|sec x + tan x|) + ln |sec x| + C

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"with these type antiderivatives, a surprising amount of information is hidden in the constant. What I mean is that both my antiderivative and the one in the book are valid, and they only differ by a constant.
Its not uncommon for these types of integrals
Just because two antiderivatives dont look the same doesnt mean one is wrong
"

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<@&791435371564892232>

dense sage
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No

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Use the substitution

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Sub back in ure u and u get what is required

steel glen
# dense sage

but when i integrated with wolfram they gave this as well ln (|sec x + tan x|) + ln |sec x| + C

dense sage
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Same thing probs

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Just simplify thT in terms of sin

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See if u get the same

steel glen