Tabel de integrale nedefinite

  1. \(\int dx=x+C,x\in \mathbb{R}\)
  2. \(\int x^{\alpha }dx=\frac{x^{\alpha +1}}{\alpha +1}+C,x\in \left ( 0,+\infty \right ),\alpha \neq -1\)
  3. \(\int a^{x}dx=\frac{a^{x}}{lna}+C,x\in \mathbb{R}\)
  4. \(\int e^{x}dx=e^{x}+C,x\in \mathbb{R}\)
  5. \(\int \frac{1}{x}dx=ln\left | x \right |+C,x\in I\subset \mathbb{R}^{*}\)
  6. \(\int \frac{1}{x^{2}-a^{2}}dx=\frac{1}{2a}ln\left | \frac{x-a}{x+a} \right |+C, x\in I\subset \mathbb{R}\setminus \left \{ \pm a \right \},a\neq 0\)
  7. \(\int \frac{1}{x^{2}+a^{2}}dx=\frac{1}{a}arctg\frac{x}{a}+C,x\in \mathbb{R},a\neq 0\)
  8. \(\int \frac{1}{\sqrt{a^{2}-x^{2}}}dx=arcsin\frac{x}{a}+C,x\in \left ( -a,a \right ),a\neq 0\)
  9. \(\int sinxdx=-cosx+C,x\in \mathbb{R}\)
  10. \(\int cosxdx=sinx+C,x\in \mathbb{R}\)
  11. \(\int \frac{1}{sin^{2}x}dx=-ctgx+C,x\in I\subset \mathbb{R}\setminus \left \{ k\pi \right \}\)
  12. \(\int \frac{1}{cos^{2}x}dx=tgx+C,x\in I\subset \mathbb{R}\setminus \left \{ \left ( 2k+1 \right )\frac{\pi }{2} \right \}\)
  13. \(\int tgxdx=-ln\left | cosx \right |+C,x\in I\subset \mathbb{R}\setminus \left \{ \left ( 2k+1 \right ) \frac{\pi }{2}\right \}\)
  14. \(\int ctgxdx=ln\left | sinx \right |+C,x\in I\subset \mathbb{R}\setminus \left \{ k\pi \right \}\)
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