Evaluate the following integral. etan⁡xcos2xdx

jamessinatraaa

jamessinatraaa

Answered

2022-01-02

Evaluate the following integral.
etanxcos2xdx

Answer & Explanation

movingsupplyw1

movingsupplyw1

Expert

2022-01-03Added 30 answers

Step 1
Given integral is
etanxcos2xdx
We know that secx=1cosx
Therefore, given integral can be written as
etanxcos2xdx=etanx(sec2xdx)
Step 2
Now, we will use the following substitution to evaluate the integral
tanx=t
sec2xdx=dt
Therefore, we have
etanxcos2xdx=etdt
etanxcos2xdx=et+c
etanxcos2xdx=etanx+c
Step 3
Ans:
etanxcos2xdx=etanx+c

Annie Gonzalez

Annie Gonzalez

Expert

2022-01-04Added 41 answers

Given:
etan(x)cos(x)2dx
1dt
Use 1dx=x to evaluate the integral
t
Substitute back
etan(x)
Add C
Answer:
etan(x)+C
Vasquez

Vasquez

Expert

2022-01-07Added 457 answers

etan(x)cos(x)2dx
We put the expression 1/cos(x)2 under the differential sign, i.e.:
1cos(x)2dx=d(tan(x)),t=tan(x)
Then the original integral can be written as follows:
etdt
This is a tabular integral:
etdt=et+C
To write down the final answer, it remains to substitute tan(x) instead of t.
etan(x)+C

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