Standardintegraler
| Standardintegraler | |
| \[ \int \mathrm{d}x=x+c \] |
\[ \int k\mathrm{d}x=kx + C\] |
| \[ \int x^n\mathrm{d}x=\frac{x^{n+1}}{n+1}+ C,\, n\ne -1 \] |
\[ \int \frac{1}{x}\mathrm{d}x=\ln|x|+ C \] |
| \[ \int \cos(x)\mathrm{d}x=\sin(x)+ C \] |
\[ \int\sin(x)\mathrm{d}x=-\cos(x)+ C \] |
| \[ \int \tan(x)\mathrm{d}x=-\ln|\cos(x)| + C \] |
\[ \int \mathrm{e}^x\mathrm{d}x=\mathrm{e}^x + C \] |
| \[ \int a^x\mathrm{d}x=\frac{a^x}{\ln(a)} + C \] |
\[ \int \ln(x)\mathrm{d}x=x\ln(x)-x + C \] |
| \[ \int \frac{\mathrm{d}x}{\sqrt{a^2+x^2}}=\ln(\sqrt{a^2+x^2}+x) + C \] | \[ \int \frac{\mathrm{d}x}{ax+b} =\frac{1}{a}\ln|ax+b| + C\] |
| \[ \int \frac{\mathrm{d}x}{a^2-x^2}=\frac{1}{2a}\ln \left| \frac{x+a}{x-a}\right| + C\] |
\[ \int \frac{\mathrm{d}x}{\cos^2(x)}=\tan(x) + C \] |
| \[ \int \frac{\mathrm{d}x}{\sin^2(x)}=-\frac{1}{\tan(x)} + C \] |
\[ \int\frac{\mathrm{d}x}{a^2 -x^2} =\frac{1}{2a}\ln\left|\frac{a+x}{a-x}\right| + C\] |
| \[ \int \sinh(x)\mathrm{d}x=\cosh(x) + C \] |
\[ \int \cosh(x)\mathrm{d}x=\sinh(x) + C \] |
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