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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Indefinite Integration

NDA 2012 · Mathematics · Indefinite Integration

What is ∫ a^x e^x d x equal to?

What is ∫axexdx\int a^x e^x d x equal to?

Options

  1. Aaxexln⁡a+c\frac{a^x e^x}{\ln a}+c
  2. Baxex+ca^x e^x+c
  3. Caxexln⁡(ae)+c\frac{a^x e^x}{\ln (a e)}+c
  4. DNone of the above where cc is the constant of integration.

Correct answer

C. axexln⁡(ae)+c\frac{a^x e^x}{\ln (a e)}+c

Step-by-step solution

∫axexdx=∫(aex)dx=(ae)xlog⁡e(ae)+c\int a^x e^x d x=\int\left(a e^x\right) d x=\frac{(a e)^x}{\log _e(a e)}+c
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