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Question Number 104071 by DGmichael last updated on 19/Jul/20

Answered by Dwaipayan Shikari last updated on 19/Jul/20

$$\int 6\sqrt{t^2+t+\frac{1}{4}}dt$$$$6\int \sqrt{{(t^2+\frac{1}{2})}^2}dt$$$$6\int (t^2+\frac{1}{2})dt=2t^3+3t+Constant$$

Answered by bobhans last updated on 19/Jul/20

$$36t^4+36t^2+9={(6t^2+3)}^2>0,\mathrm{\forall }t\in \mathbb{R}$$$$\int \sqrt{{(6t^2+3)}^2}dt=2t^3+3t+C$$

Commented by DGmichael last updated on 19/Jul/20

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