Formula. Math
Integrals
- The integrals of rational functions
\(\int x^{n} dx \ldots \int {dx \over x(x^2+px+q)}\) - Integrals containing logarithm
\(\int \ln x\,dx \ldots \int x\ln(x+\sqrt{x^2-a^2}) dx\) - Integrals containing the exponent
\(\int e^x dx \ldots \int e^{ax} \cos^2 x \, dx\) - Some naberushkina integrals
\(\int e^{\pm x^2} dx \ldots \int e^x \ln x \, dx\) - The integrals of irrational functions
\(\int {x^n dx} \ldots \int {dx \over x^3\sqrt{x^2-a^2}}\)
Trigonometry
- Basic formulas
\(\sin^2 \alpha + \cos^2 \alpha \ldots \mathtt{ctg} \left(\alpha \pm \beta \right)\) - The sum or difference of functions of multiples of angles
\(\sin \alpha \pm \sin \beta \ldots \mathtt{ctg} 3\alpha\) - The product of the degree functions
\(\sin \alpha \cdot \sin \beta \ldots \cos^5\alpha\) - Useful identities
\(\sum \sin(kx) \ldots \prod \cos \left({\frac{x}{2^{k}}}\right)\) - Useful identities (2)
\(\sin^4(x)+\cos^4(x) \ldots \mathtt{arctg}\left (\frac 12 \right)+\mathtt{arctg}\left (\frac 13 \right)\) - The sum and difference of inverse functions
\(\arcsin x + \arcsin y \ldots \arctan \frac12 + \arctan \frac13\)