ПОМОГИТЕ РЕШИТЬ ОПРЕДЕЛЕННЫЙ ИНТЕГРАЛ

Решите задачу:

$\int _0^2(2^{x}-2^{\frac{x}{2}})dx=\int _0^22^{x}dx-\int _0^22^{\frac{x}{2}}dx=\frac{2^{x}}{ln2}|_0^2-2\int _0^22^{\frac{x}{2}}\cdot \frac{1}{2}dx=\\\\=\frac{2^2}{ln2}-\frac{2^0}{ln2}-2\int _0^22^{\frac{x}{2}}\cdot d(\frac{x}{2})=\frac{4}{ln2}-\frac{1}{ln2}-2\cdot \frac{2^{\frac{x}{2}}}{ln2}|_0^2=\\\\=\frac{3}{ln2}-2(\frac{2}{ln2}-\frac{1}{ln2})=\frac{3}{ln2}-\frac{2}{ln2}=\frac{1}{ln2}\\\\\\\int 2^{ \frac{x}{2}}\cdot d(\frac{x}{2})=\int 2^t\cdot dt=\frac{2^{t}}{ln2}+C=\frac{2^{\frac{x}{2}}}{ln2}+C$