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Question Number 89025 by M±th+et£s last updated on 14/Apr/20

∫((3^x +4^x )/5^x )dx

$$\int\frac{\mathrm{3}^{{x}} +\mathrm{4}^{{x}} }{\mathrm{5}^{{x}} }{dx} \\ $$

Answered by $@ty@m123 last updated on 14/Apr/20

∫((3/5))^x dx+∫((4/5))^x dx  =((((3/5))^x )/(ln ((3/5))))+((((4/5))^x )/(ln ((4/5)))) +C

$$\int\left(\frac{\mathrm{3}}{\mathrm{5}}\right)^{{x}} {dx}+\int\left(\frac{\mathrm{4}}{\mathrm{5}}\right)^{{x}} {dx} \\ $$$$=\frac{\left(\frac{\mathrm{3}}{\mathrm{5}}\right)^{{x}} }{\mathrm{ln}\:\left(\frac{\mathrm{3}}{\mathrm{5}}\right)}+\frac{\left(\frac{\mathrm{4}}{\mathrm{5}}\right)^{{x}} }{\mathrm{ln}\:\left(\frac{\mathrm{4}}{\mathrm{5}}\right)}\:+\mathrm{C} \\ $$

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