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Lösung 2.2:2c

Aus Online Mathematik Brückenkurs 2

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Zeile 11: Zeile 11:
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<math>du=\left( \text{3}x+\text{1} \right)^{1}\,dx=3\,dx</math>
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<math>du=\left( \text{3}x+\text{1} \right)^{\prime }\,dx=3\,dx</math>

Version vom 12:39, 20. Okt. 2008

If we focus on the integrand, then the substitution u=3x+1 seems suitable, since we then get u  which we can integrate. There is also no risk involved in using a linear substitution such as u=3x+1, because the relation between dx and du will be a constant factor,


du=3x+1dx=3dx 


which does not cause any problems.

We obtain


503x+1dx=u=3x+1du=3dx=31161udu=31161u12du=31u21+121+1116=3132uu116=921616−11=92164−1=9263=14

Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_2.2:2c“