∫a^x+ b^xc^x dx = ∫(Ac)^x + (bc)^x dx = (ac)^xlog(ac)log(ac) + (bc)^xlog(bc)+c =1c^x(a^xlog(ac) + b^xlog(bc))+c ...

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Property 4

Integrate ∫...

Question

Integrate $\int \frac{a^{x} + b^{x}}{c^{x}} d x$

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Solution

$\int \frac{a^{x} + b^{x}}{c^{x}} d x = \int {(\frac{A}{c})}^{x} + {(\frac{b}{c})}^{x} d x = \frac{{(\frac{a}{c})}^{x}}{log (\frac{a}{c})} log (\frac{a}{c}) + \frac{{(\frac{b}{c})}^{x}}{log (\frac{b}{c})} + c$
$= \frac{1}{c^{x}} ⎛ ⎜ ⎜ ⎜ ⎜ ⎝ \frac{a^{x}}{log (\frac{a}{c})} + \frac{b^{x}}{log (\frac{b}{c})} ⎞ ⎟ ⎟ ⎟ ⎟ ⎠ + c$

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