Find the indefinite integral. \int \frac{e^{\frac{1}{t}}}{t^{2}}dt

Juan Hewlett 2021-12-19 Answered
Find the indefinite integral.
e1tt2dt
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Expert Answer

Papilys3q
Answered 2021-12-20 Author has 34 answers
Step 1
Given: I=e1tt2dt
for evaluating given integral, in given integral we substitute
1t=p...(1)
now, differentiating equation(1) with respect to t
so,
ddt(1t)=ddt(p)   (ddx(1x)=1x2)
=1t2=dpdt
dtt2=dp
Step 2
now, replacing 1t with p, dtt2 with -dp in given integral and integrate it
so,
e1tt2dt=epdp   (exdx=ex+c)
=ep+c...(2)
now, substitute p=1t in equation(2)
so,
e1tt2dt=e1t+c
hence, given integral is equal to e1t+c.

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movingsupplyw1
Answered 2021-12-21 Author has 30 answers
Given:
e1tt2dt
=eudu
Now we calculate:
eudu
Integral of exponential function:
audu=auln(a) at: a=e
=eu
We substitute the already calculated integrals:
eudu
=eu
=e1t
Answer:
=e1t+C

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nick1337
Answered 2021-12-28 Author has 575 answers

e1tt2dt
eudu
eudu
eu
e1t
Add C
Result:
e1t+C

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