Question

$\int e^{x\log a}\cdot e^{x}dx$ is equal to

• (A) $\frac{a^x}{\log ae}+c$
• (B) $\frac{a^x}{1+{\log }_{e}a}+c$
• (C) ${\mathrm{lae}|}^x+c$
• (D) $\frac{\mid a{e}^x}{{\log }_{e}ae}+c$

Answer 1

The Correct Option is D

Explanation:
Let $I=\int e^{x\log a}\cdot e^{x}dx$$=\int a^x\cdot e^{x}dx=\int (ae{)}^{x}dx$$=\frac{(ae{)}^x}{{\log }_{e}ae}+c$