Question

Calculator question: Integral of (e^x^2-2x)/e^x^2 dx
Answer is x+e^-x^2+C
Please show work on how to get to the answer! Thank you

Answer 1

Notice that
\[
\frac{e^{x^2}-2
x}{e^{x^2}}=e^{-x^2}
\left(e^{x^2}-2 x\right)=1-2
e^{-x^2} x
\]
Can you finish it now?

Answer 2

\[\Large
\int \left(1-2 e^{-x^2} x\right)
\, dx=e^{-x^2}+x +C
\]

Answer 3

Okay so e^-x^2 times e^x^2 =1...how did you get the integral of 2e^-x^2 x?

Answer 4

If you take the integral of -2e^-x^2 x you would get -2e^-x^2 x^2/2 so the 2 will cancel but you would still have x^2 attached

Answer 5

Put
\[
u=-x^2\\
du= -2 x dx\\
\int -2e^{-x^2} x dx =\int e^u du= e^u + C= e^{-x^2} + C
\]