$$\int \frac{\sin 2 x}{(a+b \cos x)^2} d x=$$

If $m_1$ and $m_2$ are the slopes of the lines represented by $a x^2+2 h x y+b y^2=0$ satisfying the condition $16 \mathrm{~h}^2=25 \mathrm{ab}$, then ............ .

The modulus of the square root of the conjugate of $-7+24 \sqrt{-1}$ is __________

If $x+\log _{15}\left(5+3^x\right)=x \log _{15} 5+\log _{15} 24, \quad$ then $x=$ _________