In the given equation as follows , use a table

hunterofdeath63 2021-12-10 Answered
In the given equation as follows , use a table of integrals with forms involving the trigonometric functions to find the indefinite integral:
11+e2xdx
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Expert Answer

Bertha Jordan
Answered 2021-12-11 Author has 37 answers

Step 1
Let 1+e2x=t. Differentiate both sides.
e2x×2dx=dt
dx=dt2e2x
=dt2(t1)
Substitute the values into the integral. Also since the integral is indefinite; a constant of integration is to be added.
Step 2
Perform the integration.
11+e2xdx=1t×dt2(t1)
=12dtt(t1)
=12[1t11t]dt
=12×[ln|t1|ln|t|]+c
=12×[ln|1+e2x1|ln|1+e2x|]+c
=12×[ln|e2x|ln|1+e2x|]+c
Hence the solution is obtained.

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SlabydouluS62
Answered 2021-12-12 Author has 52 answers
1e2x+1dx
=121eu+1du
=eueu+1du
=1vdv
=ln(v)
=ln(eu+1)
121eu+1du
=ln(eu+1)2
Answer:
=ln(eu+1)2+C
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