∫（x^5+5^x)dx;∫x2^x²dxevaluate the integral. Thank you.
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(1) ∫ (x^5 + 5^x)dx
= ∫ x^5 dx + ∫ 5^x dx
= (1/6)(x^6) + (1/ln 5)(5^x) + C
(2) Let x^2 = u then 2x dx = du
x dx = du/2
∫ x 2^(x^2) dx = ∫ (2^u)(du/2)
= (1/2)(2^u)(1/ln 2) + C
= (1/ln 4)(2^(x^2)) + C
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