Question

Solve $\int 2^{{\log }_{4}x}dx.$

Answer 1

According to question,

$\int 2^{lo{g}_4^x}dx$

$⟹\int x^{lo{g}_4^2}dx$

$⟹\int x^{\frac{1}{2}lo{g}_2^2}dx$

$⟹\int x^{\frac{1}{2}}dx$

$⟹\frac{2}{3}{x}^{3/2}+C$