tzhang

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These are questions asked by tzhang

If I let Maple computer the integral of tan(x), it gets

Int(tan(x), x)=int(tan(x),x), which is the same result as many other softwares get.

However, if I do integral of tan(2*x), it becomes

Int(tan(2*x), x)=(1/4)*ln(1+tan(2*x)^2), instead of -(1/2)*ln(cos(2*x)). The latter form should make more sense considering what Maple gives for tan(x).

In fact, Maple alwys gives the anwer ln(1+tan(n*x)^2)/(2*n) (1) as the integral for tan(n*x) when n>=2. While this is also an indefinite integral of tan(n*x), it is not exactly the equivalent of -(1/n)*ln(cos(n*x)) (2), which is the form Maple gives for integral of tan(x). Expression (2) sometimes evaluates to complex values while (1) only evaluates to real values. It seems that for integral of tan(2x) Maple tries to find the antiderivative that always evaluates to real values, but for tan(x) Maple is happy with -ln(cos(x)), whose value may be complex.

Is there a reason why Maple does this? And is there any way to change the way Maple computes indefinite integrals?

I hope to enter something like

5^(x-1)=5^x/5

And get "true". Mathematica and some other softwares do this but Maple returns my exact input (I'm new to Maple).

I tried using evalb and verify, but they all return false or FAIL. Is there a straightforward to verify equality and get a result of True or False in Maple?

Thanks!

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