Question

integral of e^3xsinx

Answer 1

is this correct?

Answer 2

There is a technique to solve this type of integrals, as you know, derivative of sin is cos and cos is again sin, then you can do this by letting your integral as some variable like \(I\)..

Answer 3

my instructions say to do it by parts, i did use the I thing though

Answer 4

Yeah, obviously it is by parts..

Derivative of sin(x) is -cos(x) ??? :)

Answer 5

ffs! i got the derivative and integral confused

Answer 6

Correct that now.. :P

Answer 7

you have to take derivative of \(u\) and integral of \(v\).

Answer 8

It is correct if I neglect the mistakes of \(-ve\) signs.. Good.. :)

Answer 9

I am giving you general formula : you can verify your result using this general result:

\[\int\limits e^{bx} \cdot \sin(ax) \cdot dx = \frac{e^{bx}}{a^2 + b^2}(b \sin(ax) - a \cos(ax))\]

Answer 10

In your question, when you compare with it, \(a = 1\) and \(b = 3\)..

Answer 11

Just do as you have done earlier, only thing you have to do is just be careful with negative signs.. I know you will do this correctly..

I said earlier, be slow but accurate as well.. :P