Title: Integration #3
Course: Demonstrating STACK (v4.4.7)

Evaluate the following improper integral if possible.
\[ \int^0_{-\infty} [value] [value] e^{[value][value]} d[value] \]
If the integral cannot be evaluated enter 99999 (5 9's).
Feedback: To solve this integral use the formula for integration by parts,\( \int u\frac{dv}{dx}dx= uv-\int v\frac{du}{dx}dx\) Let\[u = [value][value] , \frac{dv}{d[value]} = e^{[value][value]}\] Then \[\int[value] [value] e^{[value][value]}d[value] = \frac{[value][value]e^{[value][value]}}[value]-\int \frac{[value]e^{[value][value]}}[value] = [value] \] Hence \[\int^0_{-\infty}[value] [value] e^{[value][value]}d[value] = \left[[value]\right]^0_{-\infty} = [value]\]

Evaluate the following improper integral if possible.
\[ \int^[value]_0 \frac{1}{[value]^\frac[value][value]}\, d[value] \]
If the integral cannot be evaluated enter 99999 (5 9's).
Feedback: \[\int^[value]_0 [value] d[value] = \left[[value]\right]^[value]_0 = [value]-[value] = [value]\]