Solve ∫ sinx+cosx/tan^2x+7 wrt x

$$\int \frac { \sin x + \cos x } { \tan ^ { 2 } x + 7 } d x$$

Evaluate

$$\frac{\sqrt{42}\ln(\frac{|\sin(x)-\sqrt{42}|}{|\sin(x)+\sqrt{42}|})}{14}+\frac{\sqrt{6}\arctan(\sqrt{6}\cos(x))}{36}+\frac{\sin(x)}{6}-\frac{\cos(x)}{6}+С$$

Differentiate w.r.t. x

$$\frac{\cos(x)\left(-84\cos(x)|\sin(x)-\sqrt{42}|\left(\sin(x)\right)^{3}+36\sqrt{42}\sin(x)|\sin(x)-\sqrt{42}|\left(\cos(x)\right)^{2}+1512\sqrt{42}sign(\sin(x)-\sqrt{42})\left(\cos(x)\right)^{2}-6\sqrt{42}sign(\sin(x)-\sqrt{42})\left(\sin(x)\right)^{2}-9\sqrt{42}sign(\sin(x)-\sqrt{42})\left(\sin(2x)\right)^{2}+2016|\sin(x)-\sqrt{42}|\left(\cos(x)\right)^{2}-14|\sin(x)-\sqrt{42}|\left(\sin(x)\right)^{2}-21|\sin(x)-\sqrt{42}|\left(\sin(2x)\right)^{2}+6\sqrt{42}\sin(x)|\sin(x)-\sqrt{42}|+1764\sin(2x)|\sin(x)-\sqrt{42}|+252\sqrt{42}sign(\sin(x)-\sqrt{42})+336|\sin(x)-\sqrt{42}|\right)}{84|\sin(x)-\sqrt{42}|\left(-\left(\sin(x)\right)^{2}+42\right)\left(6\left(\cos(x)\right)^{2}+1\right)}$$