Evaluate the definite integral. \int_{1}^{2}\frac{e^{\frac{1}{x^{4}}}}{x^{5}}dx

Priscilla Johnston 2021-12-21 Answered
Evaluate the definite integral.
12e1x4x5dx
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Expert Answer

Anzante2m
Answered 2021-12-22 Author has 34 answers

Step 1
To evaluate the definite integral.
Step2
Given information:
12(e1x4x5)dx
Step 3
Calculation:
Integrate the function with respect to x.
12(e1x4x5)dx
Let 1x4=u
so, differentiate with respect to x.
ddx(1x4)=ddx(u)
4x5=dudx
(1x5)dx=14du
[put in the given integral]
Step 4
So, the integral become,
x=12(e1x4x5)dx=x=12(eu4)du
[put(1x5)dx=(1x4)du,andu=1x4]
=14[eu]x=12
[exdx=ex]
=14[e1x4]x=12
[substitute u=1x4]
=14[e12(4)e11(4)]

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limacarp4
Answered 2021-12-23 Author has 39 answers
Step 1
Let u=1x4 so that du=4x5dx
By substitution,
e1x4x5dx=eu(14du) (1)
e1x4x5dx=14eudu
Recall: eudu=eu+C so:
e1x4x5dx=14eu+C
e1x4x5dx=14e1x4+C
Hence,
12e1x4x5dx=[14e1x4]12
=14e124(14e114)
=14e116+14e
=14(e116+e)
0.413
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nick1337
Answered 2021-12-28 Author has 510 answers

Step 1
We have to calculate
12e1x4x5dx
Let us first calculate indefinite integral.
Given integral
Step 2
e144x5dx=14eudu
Substitute u=1x4 this gives us
dx=x54du
Step 3
14eudu=eu4=e1x44
Substitute back u=1x4
Step 4
e1x4x5dx=e1454+C
12e1x4x5dx=[e1454]12
=e4e164

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