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Question Number 118270 by bramlexs22 last updated on 16/Oct/20

$$\int x{a}^x{(1-a)}^{1-x}dx?$$

Commented by Dwaipayan Shikari last updated on 16/Oct/20

$$(1-a)\int x{\left(\frac{a}{(1-a)}\right)}^x$$$$\frac{1-a}{log\left(\frac{a}{1-a}\right)}x{\left(\frac{a}{1-a}\right)}^x-\frac{1-a}{log\left(\frac{a}{1-a}\right)}\int {\left(\frac{a}{1-a}\right)}^x$$$$\frac{1-a}{log\left(\frac{a}{1-a}\right)}x{\left(\frac{a}{1-a}\right)}^x-\frac{1-a}{{log}^2\left(\frac{a}{1-a}\right)}.{\left(\frac{a}{1-a}\right)}^x+C$$$$\left(\frac{1-a}{log\left(\frac{a}{1-a}\right)}{\left(\frac{a}{1-a}\right)}^x\right).(x+\frac{1}{log\left(\frac{a}{1-a}\right)})+C$$

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