Question | Answer |
\[ \int \sin x \] | \[ -\cos x + C \] |
\[ \int \cos x \] | \[ \sin x + C \] |
\[ \int \frac{1}{x} \] für \(x<0\) | \[ \ln(-x) + C \] |
\[ \int \frac{1}{x} \] für \(x>0\) | \[ \ln(x) + C \] |
\[ \int e^x \] | \[ e^x + C \] |
\[ \int e^{ax+b} \] für \(a \neq 0\) | \[ \frac{1}{a} e^{ax+b} + C \] |
\[ \int x^n dx \] | \[ \frac{x^{n+1}}{n+1} + C \] |
\[ \int (ax+b)^n dx \] | \[ \frac{1}{a} \cdot \frac{(ax+b)^{n+1}}{n+1} + C \] für \( n \neq -1\) |
\[ \int \frac{1}{ax+b} \] für \(ax+b>0, a \neq 0\) | \[ \frac{1}{a} \ln(ax+b) + C \] |
\[ \int \frac{1}{ax+b} \] für \(ax+b<0, a \neq 0\) | \[ \frac{1}{a} \ln(-ax-b) + C \] |
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