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# Integration

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I used trigonometric substitution and ended up with       integral of (secθ)/(tan^2θ)

then I stuck there

xvxvxv  Feb 25, 2015

#5
+889
+10

Yes, that's correct.

But you now have to shift your result back in terms of x.

Bertie  Feb 25, 2015
Sort:

#1
+889
+10

Just keep going. Put what you have in terms of cos and sin.

You might then simply spot the integral (think of the function of a function rule for differentiation), but if you can't use the (second) substitution $$u=\sin\theta$$.

Bertie  Feb 25, 2015
#2
+1832
0

I tried but I can't .. ><

xvxvxv  Feb 25, 2015
#3
+889
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Think of cos and sin as being the basic trig functions.

The other four, tan, cot, sec and cosec can each be expressed in terms of them. That means that any expression involving trig functions can be written using cos and sin only.

Do that for your   $$\sec\theta/\tan^{2}\theta$$ and post your result.

Bertie  Feb 25, 2015
#4
+1832
0

it will be -cscθ +c

right  ?

xvxvxv  Feb 25, 2015
#5
+889
+10

Yes, that's correct.

But you now have to shift your result back in terms of x.

Bertie  Feb 25, 2015
#6
+1832
+5

yes now its very clear ..

thank you =)

xvxvxv  Feb 25, 2015

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