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junior college 2 | H3 Maths

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(Undergraduate integral calculus)

Hello, what's the logic or thought process behind using hyperbolic sine as the inverse substitution instead of a normal trigo function? The integrand (after substituting u and u' as e^x) is of the form sqrt(a^2 + x^2), so shouldn't x = atan(t) be used instead?

[Answer: pi(arcsinh(e) - arcsinh(1) + (e)sqrt(1+e^2) - sqrt(2))]

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