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Today's calculation of Integral 735

Source: 2011 Miyazaki University entrance exam/Agriculture

July 3, 2011
calculusintegrationtrigonometrylogarithmscalculus computations

Problem Statement

Evaluate the following definite integrals:
(a) ∫0π2xtan⁡(x2) dx\int_0^{\frac{\sqrt{\pi}}{2}} x\tan (x^2)\ dx
(b) ∫013xe3x dx\int_0^{\frac 13} xe^{3x}\ dx
(c) ∫eee1xln⁡x dx\int_e^{e^e} \frac{1}{x\ln x}\ dx
(d) ∫23x2+1x(x+1) dx\int_2^3 \frac{x^2+1}{x(x+1)}\ dx
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