Løs [ ∫ sec^2(x/3-pi/8)+4/5+(x-1)^2+(x/4-1)^2]d

$$[ \int \sec ^ { 2 } ( \frac { x } { 3 } - \frac { \pi } { 8 } ) + \frac { 4 } { 5 + ( x - 1 ) ^ { 2 } } + ( \frac { x } { 4 } - 1 ) ^ { 2 } ] d$$

Evaluer

$$\frac{d\left(192\sqrt{5}\arctan(\frac{\sqrt{5}\left(x-1\right)}{5})+720\tan(\frac{8x-3\pi }{24})+5\left(x-4\right)^{3}+240С\right)}{240}$$

Differentier w.r.t. x

$$\frac{d\left(x^{4}\left(\cos(\frac{8x-3\pi }{24})\right)^{2}+38\left(x\cos(\frac{8x-3\pi }{24})\right)^{2}-10x^{3}\left(\cos(\frac{8x-3\pi }{24})\right)^{2}-80x\left(\cos(\frac{8x-3\pi }{24})\right)^{2}+160\left(\cos(\frac{8x-3\pi }{24})\right)^{2}+16x^{2}-32x+96\right)}{16\left(x^{2}-2x+6\right)\left(\cos(\frac{8x-3\pi }{24})\right)^{2}}$$