_ ^ ( e^ a x + e^ x a )dx = - Vidyadip

MCQ

$\int_{}^{} {({e^{a\log x}} + {e^{x\log a}})dx} = $

A
${x^{a + 1}} + \frac{{{a^x}}}{{\log a}} + c$
B
$\frac{{{x^{a + 1}}}}{{a + 1}} + {a^x}\log a + c$
✓
$\frac{{{x^{a + 1}}}}{{a + 1}} + \frac{{{a^x}}}{{\log a}} + c$
D
None of these

✓

Answer

Correct option: C.

$\frac{{{x^{a + 1}}}}{{a + 1}} + \frac{{{a^x}}}{{\log a}} + c$

c
(c) $\int_{}^{} {({e^{a\log x}} + {e^{x\log a}})\,dx} = \int_{}^{} {({e^{{{\log }_e}{x^a}}} + {e^{{{\log }_e}{a^x}}})\,dx} $
$ = \int_{}^{} {({x^a} + {a^x})\,dx} = \frac{{{x^{a + 1}}}}{{a + 1}} + \frac{{{a^x}}}{{\log a}} + c$.

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