- #1

vande060

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## Homework Statement

sorry wait a few moments for the details, i hit post on accident prematurely

∫ √(1 + x^2)/x dx

## The Attempt at a Solution

∫ √(1 + x^2)/x dx

x = tanϑ , dx sec^2ϑ dϑ -π/2 < ϑ < π/2

√(1 + x^2) = secϑ

∫ (secϑ * sec^2ϑ dϑ )/ tanϑ dϑ

after using trig identities

∫cscϑ dϑ + ∫ tanϑsecϑ dϑ

= -Ln I cscϑ + cotϑ I + secϑ + C

= -LnI [√(1 + x^2) +1]/xI + √(1 + x^2) + C

but the back of the book tells me

= LnI [√(1 + x^2) - 1]/xI + √(1 + x^2) + C

am i missing something here

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