Hi all, I've just recently been going on maths forums to find out why this problem occurs. I understand how to work out the solution but not why the problem occurs in the first place. Anyway here it is:(adsbygoogle = window.adsbygoogle || []).push({});

Where y = cosh(x).e^x work out the general integral of y with respect to x.

As integral(uv') = uv - integral(u'v)

Say u = cosh(x), u'=sinh(x), v'=e^x, v=e^x

So integral(cosh(x).e^x) = cosh(x).e^x - integral(sinh(x).e^x) : Equation 1

Taking integral(sinh(x).e^x), u=sinh(x), u'=cosh(x), v'=e^x, v=e^x

integral(sinh(x).e^x) = sinh(x).e^x - integral(cosh(x).e^x) : Equation 2

Substituting equation 2 into equation 1

integral(cosh(x).e^x) = cosh(x).e^x - sinh(x).e^x + integral(cosh(x).e^x)

cosh(x).e^x - sinh(x).e^x = 0

cosh(x).e^x = sinh(x).e^x

cosh(x) = sinh(x)

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# Something gone horribly wrong (Integration)

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