Help with integration

[MAM]

Given: For all real numbers x, P'(x)=Q(x), Q'(x)=P(x), R(x)=P(x)/Q(x), (Q(x))^2 - (P(x))^2 = 1

Use the given information to solve the following indefinite integrals, using any appropriate integration method. (Give your answers in terms of the functions P and Q, with attempting to find explicit formulas for those functions.)

a) integral of x*P(x) dx
b) integral of R(x) dx
c) integral of (P(x))^2 - (Q(x))^2 dx

 

[medicalphysicsguy]

exponential growth?

This does seem an oddly worded problem. However I see that P'(x)=Q and Q'(x)=P and I can think of only one extremely common function where this is the case. So maybe your answer has to do with that?

 

[Deleted member 4993]

Given: For all real numbers x, P'(x)=Q(x), Q'(x)=P(x), R(x)=P(x)/Q(x), (Q(x))^2 - (P(x))^2 = 1

Use the given information to solve the following indefinite integrals, using any appropriate integration method. (Give your answers in terms of the functions P and Q, without attempting to find explicit formulas for those functions.)

a) integral of x*P(x) dx
b) integral of R(x) dx
c) integral of (P(x))^2 - (Q(x))^2 dx

I assume the question asked you ... Give your answers in terms of the functions P and Q, without attempting to find explicit formulas.....



I'll show you begining steps for (a)

\(\displaystyle \int x * P(x) dx\)
do integration by parts:

x = u

P(x) dx = dv

Now what....