MATLAB: Symbolic integration of c/(b*z-a)

symbolic integration logarithm

Dear all,
I want to integrate c/(b*tau-a) from tau=0 to tau=z with the assumptions a>0, b>0 c>0 and z<a/b.
In Maple it works:
eq1 := c/(b*tau-a); eq2 := int(eq1,tau=0..z, AllSolutions) assuming a::positive, b::positive, c::positive, z<a/b;
with the result:
c*(ln(-b*z+a)-ln(a))/b
How can I do this in MATLAB?
Thanks a lot!

Best Answer

Use the simplify function:
syms a b c tau z real
assume(a>0)
assume(b>0)
assume(c>0)
assume(z<a/b)
out1 = int( c/(b*tau-a),tau,0,z);
out2 = simplify(out1, 'Steps',20)
out2 =
(c*log(a - b*z))/b - (c*log(a))/b
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