Question

$\int 2^x\left(f^{\prime }\right(x)+f(x\left)\log 2\right)dx$ is equal to

• A. $2^x{f}^{\prime }\left(x\right)+c$
• B. $2^x\log 2+c$
• C. $2^{x}f\left(x\right)+c$
• D. $2^x+c$

Answer 1

The correct option is C $2^{x}f\left(x\right)+c$

$\int 2^x\left(f^{\prime }\right(x)+f(x\left)\log 2\right)dx$
Let $2^{x}f\left(x\right)=t\Rightarrow 2^x\left(f^{\prime }\right(x)+f(x\left)\log 2\right)dx=dt$
$\therefore \int dt=t+c=2^{x}f\left(x\right)+c$