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junior college 2 | H2 Maths
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hi can anyone help me with (b)? Thank u !!
Date Posted: 3 years ago
Views: 546
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done
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clear
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Hope this helps
Date Posted:
3 years ago
There's an error in the integration by parts. ∫ e^(e^x + x) dx won't be the same result as ∫e^(e^x + 1) dx = e^(e^x) found in (a)
I think i accidentally wrote e^(e^x + x) as e^(e^x +1) for the answer in part a)
Ahh yes.
Upon a second look, it seems like the v for the second integral was written as v' instead
Upon a second look, it seems like the v for the second integral was written as v' instead
Thank u
(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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