Question

integrate:

ʃ [e^-(1/2-t)x] / -(1/2-t)^2 dx

Answer 1

\(\Large\int \frac{e^{-(\frac{1}{2}-t)}x}{-(\frac{1}{2}-t)^2}dx\)?

Answer 2

yes

Answer 3

You're integrating with respect to \(x\), you should treat all other variables as constants. That means you can apply the power rule since \(\large \frac{e^{-(\frac{1}{2}-t)}}{-(\frac{1}{2}-t)^2}\) is just like any constant here.

Answer 4

so what is the answer?

Answer 5

\(\Large\int \frac{e^{-(\frac{1}{2}-t)}x}{-(\frac{1}{2}-t)^2}dx=\frac{e^{-(\frac{1}{2}-t)}}{-(\frac{1}{2}-t)^2}\cdot \frac{x^2}{2}+c\).

Answer 6

thats wrong

Answer 7

It can't be wrong unless the integral is not what I typed. Is \(-(\frac{1}{2}-t)x\) the exponent?

Answer 8

yes

Answer 9

That makes a difference.

Answer 10

\(\Large\int \frac{e^{-(\frac{1}{2}-t)}x}{-(\frac{1}{2}-t)^2}dx=-(\frac{1}{2}-t)\cdot \frac{e^{-(\frac{1}{2}-t)x}}{-(\frac{1}{2}-t)^2}+c\).
Now simplify.

Answer 11

thats wrong as well.