Интеграл	Равенство
\[\int{kdx}\]	\[kx+C\]
\[\int{x^ndx}\]	\[\frac{x^{n+1}}{n+1}+C\]
\[\int{\frac{dx}{x}}\]	\[ln|x|+C\]
\[\int{a^xdx}\]	\[\frac{a^x}{ln(a)}+C\]

Интеграл	Равенство
\[\int{sin(x)}dx\]	\[-cos(x)+C\]
\[\int{cos(x)}dx\]	\[sin(x)+C\]
\[\int{tg(x)}dx\]	\[-ln|cos(x)|+C\]
\[\int{ctg(x)}dx\]	\[ln|sin(x)|+C\]

Интеграл	Равенство
\[\int{\frac{dx}{cos^2(x)}}\]	\[tg(x)+C\]
\[\int{\frac{dx}{sin^2(x)}}\]	\[-ctg(x)+C\]
\[\int{\frac{dx}{sin(x)}}\]	\[ln|tg(\frac{x}{2})|+C\]
\[\int{\frac{dx}{cos(x)}}\]	\[ln|tg(\frac{x}{2}+\frac{\pi}{4})|+C\]

Интеграл	Равенство
\[\int{\frac{dx}{\sqrt{a^2-x^2}}}\]	\[arcsin(\frac{x}{a})+C\]
\[\int{\frac{dx}{\sqrt{a+x^2}}}\]	\[ln|x+\sqrt{a+x^2}|+C\]
\[\int{\frac{dx}{a^2+x^2}}\]	\[\frac{1}{a}arctg(\frac{x}{a})+C\]
\[\int{\frac{dx}{a^2-x^2}}\]	\[\frac{1}{2a}ln|\frac{a+x}{a-x}|+C\]

Интеграл	Равенство
\[\int{sh(x)dx}\]	\[ch(x)+C\]
\[\int{ch(x)dx}\]	\[sh(x)+C\]
\[\int{th(x)dx}\]	\[ln|ch(x)|\]
\[\int{cth(x)dx}\]	\[ln|sh(x)|\]

Правило	Равенство
\[\int{(u+v)dx}\]	\[\int{udx}+\int{vdx}\]
\[\int{kudx}\]	\[k\int{udx}\]
\[\int{udv}\]	\[uv-\int{vdu}\]
\[\int{f(\phi(x))\phi\\'(x)dx}\]	\[\int{f(\phi(x))d\phi(x)}\]

Интеграл	Равенство
\[\int{arcsin(x)dx}\]	\[x\cdot arcsin(x)+\sqrt{1-x^2}+C\]
\[\int{arccos(x)dx}\]	\[x\cdot arcsin(x)-\sqrt{1-x^2}+C\]
\[\int{arctg(x)dx}\]	\[x\cdot arctg(x)-\frac{1}{2}ln(1+x^2)+C\]
\[\int{arcctg(x)dx}\]	\[x\cdot arcctg(x)+\frac{1}{2}ln(1+x^2)+C\]

Универсальная триг. подстановка

\[x=2arctg(t), dx=\frac{2dt}{1+t^2}\] \[sin(x)=\frac{2t}{1+t^2}, сos(x)=\frac{1-t^2}{1+t^2}\]

\[\text{Нечет. от-но } sin(x)->t=cos(x)\] \[\text{Нечет. от-но } cos(x)->t=sin(x)\] \[cos(x)=sin(x)=\sqrt{1-t^2}\]

\[\text{Нечет. от-но } tg(x) \text{ или}\] \[\text{Степени sin + cos чёт. }\] \[x=arctg(t), dx=\frac{dt}{1+t^2}\] \[cos^2(x)=\frac{1}{1+t^2}, sin^2(x)=\frac{t^2}{1+t^2}\]

Триганометрические формулы

\[cos(a)cos(b)=\frac{1}{2}(cos(a+b)+cos(a-b))\] \[sin(a)sin(b)=\frac{1}{2}(cos(a-b)-cos(a+b))\] \[sin(a)cos(b)=\frac{1}{2}(sin(a+b)+sin(a-b))\] \[sin^2(x)=\frac{1}{2}(1-cos(2x))\] \[cos^2(x)=\frac{1}{2}(1+cos(2x))\]