integrate sechsqrt(x) tanhsqrt(x)/sqrt(x)

Question

I'm not quite sure on how I should approach this.

Answer 1

Hi Alex,

 

         I'll give you a few hints that should get you started.

1. let u=√x then du=1/2√x

 

2. the integrand is now 2*tanh(u)*sech(u)du

 

3.tanh(u)=sinh(u)/cosh(u) and sech(u)=1/cosh(u)

 

4. integrand is now 2*sinh(u)/cosh²(u)

 

5. try w=cosh(u) so dw=sinh(u)du

 

You should be able to get it from here.

 

Jim

 

 

Answer 2

This is a plain old u substitution.

Let u = x^1/2     than makes du = (1/2)x^-1/2 dx= 1/(2sqrt x) dx.... so 2*du = 1/(sqrt x) so replacing we get

 

integral sech u * tanh u * 2 du

 

That's equal to -2sech u + c    =    -2sech (sqrt x) + c

 

Hope this helped.