jamessinatraaa

2022-01-02

Evaluate the following integral.

$\frac{{e}^{\mathrm{tan}x}}{{\mathrm{cos}}^{2}x}dx$

movingsupplyw1

Beginner2022-01-03Added 30 answers

Step 1

Given integral is

We know that

Therefore, given integral can be written as

Step 2

Now, we will use the following substitution to evaluate the integral

Therefore, we have

Step 3

Ans:

Annie Gonzalez

Beginner2022-01-04Added 41 answers

Given:

$\int \frac{{e}^{\mathrm{tan}\left(x\right)}}{{\mathrm{cos}\left(x\right)}^{2}}dx$

$\int 1dt$

Use$\int 1dx=x$ to evaluate the integral

t

Substitute back

$e}^{\mathrm{tan}\left(x\right)$

Add C

Answer:

${e}^{\mathrm{tan}\left(x\right)}+C$

Use

t

Substitute back

Add C

Answer:

Vasquez

Expert2022-01-07Added 669 answers

We put the expression

Then the original integral can be written as follows:

This is a tabular integral:

To write down the final answer, it remains to substitute

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