Published by:
CGP EDU Academic Team
Published on: September 12, 2026
Find the value of 
.
Text Solution
Verified by ExpertsThe correct answer is:
C
To evaluate the integral \( \int (x e^x + e^x + e^e) \, dx \), we can break it into three separate integrals:
\( \int (x e^x + e^x + e^e) \ dx = (x e^x - e^x) + e^x + e^e x + C = x e^x + e^e x + C \)
Therefore, the final answer is \( x e^x + e^e x + C \).
- Step 1: Evaluate \( \int x e^x \, dx \). This can be solved using integration by parts, where we let \( u = x \) and \( dv = e^x \, dx \).
- Step 2: Applying integration by parts gives us:
\( \int x e^x \, dx = x e^x - \int e^x \, dx = x e^x - e^x + C_1 \). - Step 3: Next, evaluate \( \int e^x \, dx = e^x + C_2 \).
- Step 4: Finally, the integral of \( e^e \) is simply \( e^e x + C_3 \).
\( \int (x e^x + e^x + e^e) \ dx = (x e^x - e^x) + e^x + e^e x + C = x e^x + e^e x + C \)
Therefore, the final answer is \( x e^x + e^e x + C \).
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