Lösung 2.1:3c
Aus Online Mathematik Brückenkurs 2
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Version vom 10:17, 11. Mär. 2009
If we multiply the factors in the integrand together and use the power laws,
| \displaystyle \begin{align}
\int e^{2x}\bigl(e^x+1\bigr)\,dx &= \int\bigl(e^{2x}e^{x} + e^{2x}\bigr)\,dx\\[5pt] &= \int\bigl(e^{2x+x} + e^{2x}\bigr)\,dx\\[5pt] &= \int{\bigl(e^{3x} + e^{2x}\bigr)}\,dx\,, \end{align} |
we obtain a standard integral with two terms of the type \displaystyle e^{ax}, where \displaystyle a is a constant. The indefinite integral is therefore
| \displaystyle \int \bigl(e^{3x}+e^{2x}\bigr)\,dx = \frac{e^{3x}}{3} + \frac{e^{2x}}{2} + C\,, |
where \displaystyle C is an arbitrary constant.
