My Math Forum mathematics Q 11

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 February 6th, 2013, 11:06 PM #1 Senior Member   Joined: Oct 2009 Posts: 895 Thanks: 1 mathematics Q 11 Hi all Can please check my answer for Q11 Here are questions : http://www2.0zz0.com/2013/02/07/08/764110924.jpg my answer for 11
February 7th, 2013, 02:04 PM   #2
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Re: mathematics Q 11

Hello, r-soy!

Your algebra got tangled . . .

Quote:
 $3e^{^x}\,\! \tan y \,dx \,+\,(1\,-\,e^{^x})\sec^{^2}y\,dy \:=\:0$

$\text{W\!e have: }\e^{^x}\,-\,1)\sec^{^2}y\,dy \;=\;3e^{^x}\tan y \,dx" />

[color=beige]. . . . . . . . . . . . . . [/color]$\frac{\sec^{^2}y\,dy}{\tan y} \;=\;\frac{3e^{^x}}{e^{^x}\,-\,1}$

$\text{Integrate: }\;\;\;\;\;\;\;\int\frac{\sec^{^2}y\,dy}{\tan y} \;=\;3\int\frac{e^{^x}\,dx}{e^{^x}\,-\,1}$

[color=beige]. . . . . . . . . . . . . . [/color]$\ln|\tan y| \;=\;3\,\!\ln|e^{^x}\,-\,1|\,+\,c$

[color=beige]. . . . . . . . . . . . . . [/color]$\ln|\tan y| \;=\;\ln|e^{^x}\,-\,1|^{^3}\,+\,\ln C$

[color=beige]. . . . . . . . . . . . . . [/color]$\ln|\tan y| \;=\;\ln C|e^{^x}-1|^{^3}$

[color=beige]. . . . . . . . . . . . . . . . [/color]$\tan y \;=\;C|e^x\,-\,1|^{^3}$

 February 8th, 2013, 01:31 AM #3 Senior Member   Joined: Oct 2009 Posts: 895 Thanks: 1 Re: mathematics Q 11 thanks so much

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