Question

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

• A. $\frac{2^{2x+2}}{log2}+\frac{2^{2-3x}}{3log2}+C$
• B. $\frac{2^{2x+2}}{log2}-\frac{2^{2-3x}}{3log2}+C$
• C. $-\frac{2^{2x+2}}{2log2}-\frac{2^{2-3x}}{3log2}+C$
• D. None of these

Answer 1

Answer: (B)

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

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

$\Rightarrow I=\frac{2^{2x+3}}{2log2}+\frac{2^{2-3x}}{\left(-3\right)log2}+C=\frac{2^{2x+2}}{log2}-\frac{2^{2-3x}}{3log2}+C$