Question

General Solution i think we l be using the u substitution here but im confused can someone help

Answer 1

how do you rotate that image

Answer 2

i have tried solving it but i think im doing it all wrong

Answer 3

it is separable right ?

Answer 4

yep

Answer 5

\[\int \dfrac{\sqrt{1+x^2}}{x}dx = -\int \dfrac{\sqrt{1+y^2}}{y}dy\]

Answer 6

i need to understand the integration for this part i tried using u substitution but i think i m doing it wrong

Answer 7

did you try \(x = \tan u\) ?

Answer 8

yeah this looks very hard to integrate
https://answers.yahoo.com/question/index?qid=20090211222753AACuIJB

Answer 9

something is seriously wrong with openstudy ?

Answer 10

Try this instead :
\(x = \tan u \implies dx = \sec^2u du\)
\[
\begin{align} \int \frac{\sqrt{ 1 + x^2}}{x}\,dx & = \int\frac{\sqrt{1+\tan^2u}}{\tan u}\sec^2 udu\\ \\

& = \int \csc u \sec^2 u \,d u \\ \\ &= \int \csc u(1 + \tan^2 u)\,d u \\ \\ & = \int \csc u \,d u + \int \csc u\tan^2 u \,d u \\ \\ & = \int \csc u \,d u + \int \dfrac{\sin u}{\cos^2 u}\,d u\end{align}

\]

Answer 11

where is the square root then

Answer 12

cant we use u substitution please

Answer 13

simple u substitution doesn't seem that easy