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Writing an integral down is only the first step. A toolkit of techniques can help find its value, from substitutions to trigonometry to partial fractions to differentiation.

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Evaluate \(\displaystyle{\int_0^{3}\frac{12x+6}{x^2+x+1}dx.}\)

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Evaluate \(\displaystyle{\int_0^\frac{\pi}{32}3\tan8xdx.}\)

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Using the substitution \(u=e^{x^2},\) evaluate \(\displaystyle{\int_0^{3}12x e^{x^2}dx.}\)

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