Question

Проинтегрируйте пожалуйста

Answer 1

$intlimits{(23e^x- frac{19}{ cos^2(x)}+ frac{91}{ sqrt{1-x^2}}+17*25^x) , dx =$$intlimits{23e^x}, dx- intlimits{frac{19}{ cos^2(x)}, dx+ intlimits{frac{91}{ sqrt{1-x^2}} , dx+ intlimits{(17*25^x) , dx=$$23intlimits{e^x}, dx- 19intlimits{frac{1}{ cos^2(x)}, dx+91 intlimits{frac{1}{ sqrt{1-x^2}} , dx+ 17intlimits{25^x , dx =$$=23e^x- 19tg(x)+91arcsin(x)+ frac{17*25^x}{ln(25)}+C$

$intlimits{ frac{19^{4x}} {sqrt{1-19^{8x}}} , dx= left[begin{array}{ccc}19^{4x}=t\dt=19^{4x}*4ln(19)end{array}right]= intlimits{ frac{1} {4ln(19)sqrt{1-t^2}} , dt=$$frac{1}{4ln(19)} intlimits{ frac{1} {sqrt{1-t^2}} , dt= frac{arcsin(t)}{4ln(19)}+C=frac{arcsin(19^{4x})}{4ln(19)}+C$