Question

What's the integral of `int (tanx)*(e^x)dx`?

Answer 1

Some guidence:

Explanation:

This is a very interesting questions, but i didnt get to far finding an exact antiderivative solution, then i also tried an online integral calculator....

There is one way i can think of that can approximate a solutio:

Use the Macluaren series:

`y(x) = sum_(n=0) ^oo (y^(n)(0)* x^n)/(n!)`

Letting `y(x) = e^x * tanx`

`=> y'(x) = e^x ( tanx + sec^2 x )`

`=> y''(x) = e^x (tanx + 2sec^2 x + 2sec^2x tanx )`
.
.
.

Then evaluating each of these at `x = 0` and using the maclauren series, then integrating using power rule:

`=> int` `sum_(n=0) ^oo (y^(n)(0)* x^n)/(n!)` `dx`

Hope this was a good step in the right direction to an approximat answer!

Now here is an interesting question!:

`int` `e^x sinx` `dx` = ??

Give it a go!