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Today's calculation of Integral 879

Source: 2013 Hiroshima City University entrance exam

June 29, 2013
calculusintegrationtrigonometrycalculus computationsintegrals

Problem Statement

Evaluate the integrals as follows.
(1) ∫x22−x dx\int \frac{x^2}{2-x}\ dx
(2) ∫x5+x33 dx\int \sqrt[3]{x^5+x^3}\ dx
(3) ∫01(1−x)cos⁡πx dx\int_0^1 (1-x)\cos \pi x\ dx
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