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# simple intregration confusion watch

1. guys it lloks simple but i been getting different answers to these intrgration problems! pl help

show that ∫(x²)÷(√(x^6-1)) = 1/3 arcosh x³+ c

∫(4x)÷(√(x²+9)) = 8 + In3

thanks
2. For the first, let x³= u
3x² dx = du

= 1/31/√(u² - 1)
= 1/3arcosh u + c
= 1/3 arcosh x³+c

For the second...I get
u= x²
du = 2x dx

= ∫2/√(u + 9)

v= u+9
du = dv
= ∫2/√(v)
= 4√v
=4√(x² + 9)

Cant see how x was supposed to be eliminated in your answer...
3. thanks 4 ur help. the limits in the 2nd problem are 4 to 0.
4. done it thanks
5. (Original post by chubby)
done it thanks
How come? As your question was wrong?
6. yeah i copied the q wrongly on to TSR. The numerator was 1+4x not 4x

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