\int\limits {\frac{1}{2t^3} } \,dt<=>\frac{1}{2}\int\limits {\frac{1}{2t^2} } \,dt=>\frac{1}{2} (-\frac{1}{2(x^2+1)^2} )=-\frac{1}{4(x^2+1)^2}+C\\\int\limits {\frac{ln(x)}{x^3} } \,dx<=>\int\limits {ln(x)}(\frac{1}{x^3})\,dx=>ln(x)(-\frac{1}{2x^2} )-\int\limits {-\frac{1}{2x^2} *\frac{1}{x} }\,dx<=>ln(x)(-\frac{1}{2x^2} )+\frac{1}{2} \int\limits {\frac{1}{x^3} } \,dx=-\frac{ln(x)}{2x^2} -\frac{1}{4x^2}+C" alt="\int\limits {\frac{1}{\sqrt{4-x^2} } } \,dx =arcsin(\frac{x}{2} )+C\\\int\limits {\frac{x}{(x^2+1)^3} } \,dx;x^2+1:=t=>\int\limits {\frac{1}{2t^3} } \,dt<=>\frac{1}{2}\int\limits {\frac{1}{2t^2} } \,dt=>\frac{1}{2} (-\frac{1}{2(x^2+1)^2} )=-\frac{1}{4(x^2+1)^2}+C\\\int\limits {\frac{ln(x)}{x^3} } \,dx<=>\int\limits {ln(x)}(\frac{1}{x^3})\,dx=>ln(x)(-\frac{1}{2x^2} )-\int\limits {-\frac{1}{2x^2} *\frac{1}{x} }\,dx<=>ln(x)(-\frac{1}{2x^2} )+\frac{1}{2} \int\limits {\frac{1}{x^3} } \,dx=-\frac{ln(x)}{2x^2} -\frac{1}{4x^2}+C" align="absmiddle" class="latex-formula">