Q)
(chatquestion)...ulll 47
10:52 PM
math.stackexchange.com/c
2 Answers
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Since you asked about the indefinite integral, I
will introduce a couple of identities and
definitions:
dt
li(æ) = /
(1)
Int
li(x) = Ei(ln æ)
(2)
-t
Ei(=») = -
dt.
-x
Where li(x) is the logarithmic integral, and
Ei(x) is the exponential integral.
Start by using the substitution you attempted,
it is a good one:
x = e' + dx = e' dt
Hence giving:
e7t
· et dt
dx
In x
8t
dt
dt
dt =
Substituting u = 8t on the green integral and
applying (3), we have:
est
dt =
Ei(u) + cı = Ei
du
(8 ln æ) + c1
...
