I need to find the following intergral:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \int_{0}^{1} \frac{28x^2}{(2x+1)(3-x)} \;\; dx [/tex]

So I split it into partial fractions thus:

[tex] \frac{2}{2x+1} + \frac{36}{3-x} - 14 [/tex]

Then integrated:

[tex] \int_{0}^{1} \frac{2}{2x+1} + \frac{36}{3-x} - 14 \;\; dx [/tex]

[tex] = \left[ \ln\left| 2x+1 \right| + 12\ln\left| 2-x \right| - 14x \right]_{0}^{1} [/tex]

But this isn't going to give me the correct answer which is quoted as:

[tex]37\ln 3 - 36\ln 2 - 14 [/tex]

Can anybody see where I've gone wrong? Thank's

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# Integration using Partial Fractions

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