Beräkna
\frac{\sqrt{2}\ln(\frac{|\tan(\frac{x}{2})+1-\sqrt{2}|}{|\tan(\frac{x}{2})+\sqrt{2}+1|})}{2}+С
Derivera m.a.p. x
\frac{\sqrt{2}\left(\tan(\frac{x}{2})sign(\tan(\frac{x}{2})+1-\sqrt{2})+\sqrt{2}sign(\tan(\frac{x}{2})+1-\sqrt{2})+sign(\tan(\frac{x}{2})+1-\sqrt{2})-|\tan(\frac{x}{2})+1-\sqrt{2}|\right)\frac{\mathrm{d}}{\mathrm{d}x}(\tan(\frac{x}{2}))}{2|\tan(\frac{x}{2})+1-\sqrt{2}|\left(\tan(\frac{x}{2})+\sqrt{2}+1\right)}
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Exempel
Kvadratisk ekvation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometri
4 \sin \theta \cos \theta = 2 \sin \theta
Linjär ekvation
y = 3x + 4
Aritmetik
699 * 533
Matris
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Samtidig ekvation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiering
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Gränser
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}