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What is the value of ∫13∞1−5log3xx6dx?\displaystyle{ \int_{\frac{1}{3}}^{\infty }\frac{1-5 \log 3x}{x^6} \mathrm{d} x}?∫31∞x61−5log3xdx?
What is the value of ∫03xx(1+logx)dx?\displaystyle{ \int_{0}^{3 } x^x (1+ \log x) \mathrm{d} x}?∫03xx(1+logx)dx?
What is the value of ∫9∞(sin14x−14xcos14x)dx?\displaystyle{ \int_{9}^{\infty }\left( \sin \frac{1}{4x}- \frac{1}{4x}\cos \frac{1}{4x} \right) \mathrm{d} x}?∫9∞(sin4x1−4x1cos4x1)dx?
What is the value of ∫0π2((π2−x)sec2x−tanx)dx?\displaystyle{ \int_{0}^{ \frac{\pi}{2} } \left( \left(\frac{\pi}{2} - x \right) \sec ^2 x -\tan x \right) \mathrm{d} x}?∫02π((2π−x)sec2x−tanx)dx?
What is the value of ∫03(x−5(1+x)log(1+x)(1+x)x6)dx?\displaystyle{ \int_{0}^{3 } \left( \frac{x-5(1+x)\log (1+x)}{(1+x)x^6} \right) \mathrm{d} x}?∫03((1+x)x6x−5(1+x)log(1+x))dx?
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