Solve ∫ (3x^{15}+8x^{13}-sqrt{x^{3}}+frac{x^{12}}{4}-frac{pix^{11}}{3}+8x^10/5-4x^9/5+e^x-85^x+cosx-cscx) wrt x

$$\int ( 3 x ^ { 15 } + 8 x ^ { 13 } - \sqrt { x ^ { 3 } } + \frac { x ^ { 12 } } { 4 } - \frac { \pi x ^ { 11 } } { 3 } + \frac { 8 x ^ { 10 } } { 5 } - \frac { 4 x ^ { 9 } } { 5 } + e ^ { x } - 85 ^ { x } + \cos x - \csc x ) d x$$

Evaluate

$$-\frac{85^{x}}{\ln(85)}+e^{x}+\ln(|\cos(\frac{x}{2})|)-\ln(|\sin(\frac{x}{2})|)+\sin(x)+\frac{3x^{16}}{16}+\frac{4x^{14}}{7}+\frac{x^{13}}{52}-\frac{\pi x^{12}}{36}+\frac{8x^{11}}{55}-\frac{2x^{10}}{25}-\frac{2x^{\frac{5}{2}}}{5}+С$$

Differentiate w.r.t. x

$$\frac{\frac{30\sin(2x)}{\sin(x)}+60e^{x}-60\times 85^{x}-\frac{60}{\sin(x)}+180x^{15}+480x^{13}+15x^{12}-20\pi x^{11}+96x^{10}-48x^{9}-60x^{\frac{3}{2}}}{60}$$