J's answer to Elle's Junior College 2 H2 Maths Singapore question.
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(a)
d/dx e^(e^x) = e^x · e^(e^x)
= e^(e^x + x)
(b)
∫ e^(e^x + 2x) dx
= ∫ e^x · e^(e^x + x) dx
= e^x · e^(e^x) - ∫ e^x · e^(e^x) dx
= e^(x + e^x) - ∫ e^(e^x + x) dx
= e^(x + e^x) - e^(e^x) (see part (a))
= (e^(e^x)) (e^x - 1) + c
d/dx e^(e^x) = e^x · e^(e^x)
= e^(e^x + x)
(b)
∫ e^(e^x + 2x) dx
= ∫ e^x · e^(e^x + x) dx
= e^x · e^(e^x) - ∫ e^x · e^(e^x) dx
= e^(x + e^x) - ∫ e^(e^x + x) dx
= e^(x + e^x) - e^(e^x) (see part (a))
= (e^(e^x)) (e^x - 1) + c
Date Posted:
3 years ago
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