Question

Evaluate: $\int\frac{8^{1+x} + 4^{1-x}}{2^{x}} dx$

• A. $\frac{2^{2x+2}}{log \,2}+\frac{2^{2-3x}}{3\,log \,2}+C $
• B. $\frac{2^{2x+2}}{log\, 2}-\frac{2^{2-3x}}{3\,log \,2}+C $
• C. $-\frac{2^{2x+2}}{2\,log\, 2}-\frac{2^{2-3x}}{3\,log\, 2}+C $
• D. None of these

Answer 1

Answer: (B)

Let $I =\int\frac{8^{1+x} + 4^{1-x}}{2^{x}} dx $

$\Rightarrow I=\int\frac{2^{3x+3} +2^{2-2x}}{2^{x}} dx \Rightarrow I=\int\left(2^{2x+3}+2^{2-3x}\right)dx $

$\Rightarrow I= \frac{2^{2x+3}}{2\,log\,2}+\frac{2^{2-3x}}{\left(-3\right)\,log\,2} + C = \frac{2^{2x+2}}{log\,2}-\frac{2^{2-3x}}{3\,log\,2} + C$