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Today's calculation of Integral 885

Source:

July 15, 2013
calculusintegrationlogarithmstrigonometrycalculus computationsIndefinite integral

Problem Statement

Find the infinite integrals as follows.
(1) 2013 Hiroshima City University entrance exam/Informatic Science
∫x22−x2dx\int \frac{x^2}{2-x^2}dx
(2) 2013 Kanseigakuin University entrance exam/Science and Technology
∫x4ln⁡x dx\int x^4\ln x\ dx
(3) 2013 Shinsyu University entrance exam/Textile Science and Technology, Second-exam
∫cos⁡3xsin⁡2x dx\int \frac{\cos ^ 3 x}{\sin ^ 2 x}\ dx
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