Question

Integrate following integral:

Answer 1

\[\int\limits_{}^{}e^x e^{2x} e^{3x}...e^{200x}dx\]

Answer 2

it would just be x,2x,3x....200x

Answer 3

all have the +C part :)

Answer 4

Damn I always forget those..haha

Answer 5

\[e^x e^{2x} e^{3x}...e^{200x}=e^{x+2x+3x+\cdots+200x}\]

\[=e^{x(1+2+3+\cdots+200)}\]

Answer 6

+C

Answer 7

Nope :(

Answer 8

Try again guys :)

Answer 9

you have some kind of choices?

Answer 10

I'll give a hint, it requires a special series :)

Answer 11

\[\frac{1}{\sum_{i=1}^{200}i}e^{(\sum_{i=1}^{200}i)x}+C\]

Answer 12

law of exponential?

Answer 13

just use the equality I gave above

Answer 14

or myininaya answer ;)

Answer 15

Close myininaya :)

Answer 16

the sum is 20100

Answer 17

\[\sum_{i=1}^{200}i=\frac{200(200+1)}{2}=100(200+1)=20000+100=20100\]

Answer 18

Yes :)

Answer 19

I devised that problem myself, sorry it wasn't a challenge myininaya :(

Answer 20

lol