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junior college 2 | H2 Maths
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hi can anyone help me with (b)? Thank u !!
Date Posted: 4 years ago
Views: 555
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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
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Upon a second look, it seems like the v for the second integral was written as v' instead