1-3-x-2x-1-ln-x-dx-

Question Number 125962 by bramlexs22 last updated on 15/Dec/20

\underset{1}{\int^{3}} x^{2 x} (1 + \ln x) d x = ?

Answered by liberty last updated on 16/Dec/20

l e t x^{x} = r \to {\begin{cases} x = 1 \to r = 1 \\ x = 3 \to r = 27 \end{cases} \land d r = x^{x} (1 + \ln x) d x

I = \underset{1}{\int^{3}} x^{x} . x^{x} (1 + \ln x) d x = \underset{1}{\int^{27}} r d r

I = \frac{1}{2} {[r^{2}]}_{1}^{27} = \frac{1}{2} \times 28 \times 26 = 14 \times 26 = 364

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