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Evaluate: int(8^(1+x)+4^(1-x))/(2^x)\ dx...

Evaluate: `int(8^(1+x)+4^(1-x))/(2^x)\ dx`

Text Solution

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`I=int frac{8^{1+x}+4^{1-x}}{2^{x}} d x`
` I=int frac{2^{3 x+3}+2^{2-2 x}}{2^{x}} d x`
` I=int 2^{2 x+3}+2^{2-3 x} d x`
` I=frac{2^{2 x+3}}{2 log 2}+frac{2^{2-3 x}}{(-3) log 2}+C`
` I=frac{2^{2 x+2}}{log 2}-frac{2^{2-3 x}}{3 log 2}+C`
`
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