How do you integrate the following:
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How do you integrate the following:

[From: ] [author: ] [Date: 11-12-13] [Hit: ]
.1.2.I assume you know what cosh2 and sinh2 mean.they are imaginary........
(1)Integral (3x-4)/ (x^2 - 4x +7). and (2) Integral (sinh 2x)/(Cosh 2x+1)^2
I've tried substitution, integrating by parts etc, but these two questions are still stumping me, help anyone?

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1.) ∫(3x - 4)/(x^2 - 4x + 7) = ∫(2x + x - 4)/(x^2 - 4x + 7) dx

= ∫(2x - 4)/(x^2 - 4x + 7) dx + ∫x/(x^2 - 4x + 7) dx

= ln(x^2 - 4x + 7) + ∫(x - 2 + 2)/(x^2 - 4x + 7)

= ln(x^2 - 4x + 7) + 1/2*ln(x^2 - 4x + 7) + 2*∫dx/[(x - 2)^2 + 3]

= 3/2*ln(x^2 - 4x + 7) + 2/√3 * arctan((x - 2)/√3) + C

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this was a fun one.....

1. ((3^(3/2)) log (x^2 - 4x + 7) + 4 arctan((x-2)/(sqrt(3))))/(2^sqrt(3))

2. ((cosh2*sinh2(x) + sinh2)*log((cosh2(x) + 1) + sinh2)) / ((cosh2)^3(x) + (cosh2)^2)


I assume you know what cosh2 and sinh2 mean. they are imaginary..... you can read this article if you want to know more on substituion and so forth:

http://press.princeton.edu/books/maor/ch…

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Key it into Wolfram Alpha, it'll show you the steps.

Express the first in partial fractions.
Start with u=2x for the second.

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Wow...I thought I was having trig questions but then I saw yours...good luck!
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