calculation of three integrals

[Roshdy]

integrations

how those integrals can be performed


∫ x (inv cosh x) dx


∫ (x^8 ) ln (x^5) dx


∫ (1/x) (x^2 -25)^1.5 dx

 

[katko]

I would start with integration by parts. See:
https://en.wikipedia.org/wiki/List_of_integrals_of_inverse_hyperbolic_functions
for inverse cosh, then you can do the first. same with the second ln(a^b)=b*ln(a). Same with the third.

 

[Peter Nachtwey]

The easy way is to download wxMaxmia from Sourceforge.
wxMaxima can solve these easily.

integrate(x*acosh(x),x)$
grind(%);
x^2*acosh(x)/2-(log(2*sqrt(x^2-1)+2*x)/2+x*sqrt(x^2-1)/2)/2$

 

[bednyk]

You still need some help with this...just let me know. I can explain you how to solve it - in mathematical way.