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Question Number 67233 by prof Abdo imad last updated on 24/Aug/19

$$calculate{\int }_0^1\frac{xdx}{\sqrt{1+x^4}}$$

Commented by mind is power last updated on 24/Aug/19

$$lett=x^2=>dt=2xdx$$$${\int }_0^1\frac{dt}{2\sqrt{(1+t^2)}}=\frac{1}{2}[argsh\left(t\right){\rceil }_0^1=\frac{1}{2}ln(1+\sqrt{1+1^2})-\frac{1}{2}ln(1+\sqrt{1})=\frac{1}{2}ln\left(\frac{3}{2}\right)$$

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