Integrals- Please help me identify my mistake !

[akleron]

I've done Integral on the function but my final answer should be twice as big (should be 1/4 and not 1/8 at the at end)
I'm trying to find my mistake for hours.. any help ?

 

[Deleted member 4993]

I've done Integral on the function but my final answer should be twice as big (should be 1/4 and not 1/8 at the at end)
I'm trying to find my mistake for hours.. any help ?
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To catch your mistake - you need to do one more substitution - before performing the integration:

\(\displaystyle z = \frac{u+1}{2}\)

\(\displaystyle dz = \frac{1}{2}du\)

Now integrate....and back substitute....

 

[pka]

I've done Integral on the function but my final answer should be twice as big (should be 1/4 and not 1/8 at the at end)
I'm trying to find my mistake for hours.. any help ?
View attachment 15722View attachment 15724

If I were you then I would first use
\(\displaystyle x^4+2x^2+5=x^4+2x^2+1+5=(x^2+1)^2+4\)
Then let \(\displaystyle u=x^2+1\) so that \(\displaystyle du=2xdx\)
giving us \(\displaystyle \frac{1}{2}\int {\frac{{du}}{{{u^2} + 4}}}\)

 

[lookagain]

If I were you then I would first use

There was a typo.

\(\displaystyle x^4+2x^2+5=x^4+2x^2+1+ \ \underline4 \ =(x^2+1)^2+4\)