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Solution assignment 07 Integration of standard functions

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Assignment 7

Solve:

\displaystyle\int_{1}^{2}{(4x^2+\displaystyle\frac{2}{x})}dx

Solution

Both functions in the integrand are in the list and thus we get:

\displaystyle\int_{1}^{2}{(4x^2+\displaystyle\frac{2}{x})}dx=4\displaystyle\int_{1}^{2}{x^2}dx+2\displaystyle\int_{1}^{2}{\displaystyle\frac{1}{x}}dx=

=[4\cdot\displaystyle\frac{1}{3}x^3+6\ln(|x|)]_{1}^{2}=\displaystyle\frac{28}{3}+6\ln(2)

N.B. \ln(1)=0

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