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# Integration by substitution watch

1. I'm rubbish at integration by substitution and I just can't get it right! Plus I can't figure out how I've gone wrong either, if someone can figure out where I've gone wrong with this question please (I'll post my working from my phone now)

(Integrate) 1/(cos^2x)(1+2tanx)^2 when u=1+2tanx

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2. question 8

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3. (Original post by mica-lwe)
question 8

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1/u2 does not integrate to lnu
4. Instead of writing what dx is equal to, write it as what du is equal to
5. (Original post by TeeEm)
1/u2 does not integrate to lnu
Is that where I've gone wrong then? Is it better to take 1/2 out the integral and integrate u^-2?
6. (Original post by mica-lwe)
Is that where I've gone wrong then? Is it better to take 1/2 out the integral and integrate u^-2?
sure

then you are one step from the required answer
7. (Original post by TeeEm)
sure

then you are one step from the required answer
thankyou! Have no idea why I struggle with substitution when there's harder stuff on the paper
8. (Original post by mica-lwe)
thankyou! Have no idea why I struggle with substitution when there's harder stuff on the paper
practice
if this fails try practice
and as a back up technique try practice...

9. (Original post by TeeEm)
practice
if this fails try practice
and as a back up technique try practice...

I'll try these, thanks!
10. (Original post by mica-lwe)
I'll try these, thanks!

all the best
11. hi,

Your solution makes a good start... it is fine until the line =1/2 ∫ 1/(u^2) du

keep the half outside the integral sign to simplify things; then 1/(u^2) is the same as u^(-2) because the reciprocal of a number makes the power negative and:

∫ u^(-2) du = -1/u +c as you divide by the power then add one to it ...don't forget the constant (c).

so... 1/2 ∫ u^(-2) du = -1/2u +c and you can just swap u for the substitution you made at the start.

Hope that helps

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Updated: January 26, 2015
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