MCQ
$\int_{}^{} {\frac{{{a^{\sqrt x }}}}{{\sqrt x }}dx = } $
- A$2{a^{\sqrt x }}{\log _e}a + c$
- ✓$2{a^{\sqrt x }}{\log _a}e + c$
- C$2{a^{\sqrt x }}{\log _{10}}a + c$
- D$2{a^{\sqrt x }}{\log _a}10 + c$
✓
Answer
Correct option: B.
$2{a^{\sqrt x }}{\log _a}e + c$
b
(b) Put $\sqrt x = t \Rightarrow \frac{1}{2}\frac{1}{{\sqrt x }}\,dx = dt,$ then
$\int_{}^{} {\frac{{{a^{\sqrt x }}}}{{\sqrt x }}\,dx} = 2\int_{}^{} {{a^t}dt} = \frac{{2{a^t}}}{{{{\log }_e}a}} + c = 2{a^{\sqrt x }}{\log _a}e + c.$
(b) Put $\sqrt x = t \Rightarrow \frac{1}{2}\frac{1}{{\sqrt x }}\,dx = dt,$ then
$\int_{}^{} {\frac{{{a^{\sqrt x }}}}{{\sqrt x }}\,dx} = 2\int_{}^{} {{a^t}dt} = \frac{{2{a^t}}}{{{{\log }_e}a}} + c = 2{a^{\sqrt x }}{\log _a}e + c.$
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