how do we integrate this
xe^(x^2)

Question

how do we integrate this
xe^(x^2)

anonymous · Answer

$u=x^2,\ du=xdx$

anonymous · Answer

$$
xe^{x^2}dx\to e^udu
$$

callisto · Answer

A little amendment from above:
du = 2x dx

minatsukisaya95 · Answer

isn't du=2x
how did it become like that

minatsukisaya95 · Answer

oh ok
and then how do we solve it from that

minatsukisaya95 · Answer

sorry 
i haven't learn how to integrate this yet
so i'm clueless bout this question
i only have the basic

anonymous · Answer

You can't guess what the anti-derivative of $e^u$ is?

callisto · Answer

$$\int xe^{x^2}dx$$$$=\frac{1}{2}\int 2xe^{x^2}dx$$$$=\frac{1}{2}\int e^{x^2}(2xdx)$$
Recall:
We let u = x^2, and we know du = 2xdx
Can you change the variable in the integral?

minatsukisaya95 · Answer

alright 
so the answer would be e^(x^2)
is that it?

callisto · Answer

No

minatsukisaya95 · Answer

and then how

callisto · Answer

What would you get for $\frac{1}{2}\int e^{x^2}(2xdx)$ when you change the variable from x to u?

minatsukisaya95 · Answer

oh ok 
i get 1/2(e^(x^2))

callisto · Answer

You missed something, a constant.

minatsukisaya95 · Answer

is there any other constant other than 1/2

callisto · Answer

You need to add an arbitrary constant c, or k, whenever you find the indefinite integral.

callisto · Answer

1/2 is, in fact, the coefficient of e^(x^2)

minatsukisaya95 · Answer

ok i got it 
so the answer is 1/2(e^(x^2)) + c
isn't it correct?

callisto · Answer

It is correct.

minatsukisaya95 · Answer

yeah!!!
thank u
u help me a lot.

callisto · Answer

You're welcome.