How do you integrate
title="\int\limits \frac{e^2x}{e^x-4} dx" alt="\int\limits \frac{e^2x}{e^x-4} dx" align="absmiddle" class="latex-formula">? Thank you!
1 answer:
Answer:
eˣ + 4 ln |eˣ − 4| + C
Step-by-step explanation:
∫ e²ˣ / (eˣ − 4) dx
∫ eˣ / (eˣ − 4) eˣ dx
Use u substitution.
u = eˣ − 4
du = eˣ dx
∫ (u + 4) / u du
∫ (1 + 4/u) du
Integrate.
u + 4 ln |u| + C
Plug in:
eˣ − 4 + 4 ln |eˣ − 4| + C
eˣ + 4 ln |eˣ − 4| + C
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