Exercise
$\int_{sinx}^{tanx}\left(\sqrt{x^2+x+1}\right)dx$
Step-by-step Solution
Final answer to the exercise
$\frac{1}{2}\left(\tan\left(x\right)+\frac{1}{2}\right)\sqrt{\left(\tan\left(x\right)+\frac{1}{2}\right)^2+\frac{3}{4}}+\frac{3}{8}\ln\left|\frac{2\sqrt{\left(\tan\left(x\right)+\frac{1}{2}\right)^2+\frac{3}{4}}+2\tan\left(x\right)+1}{\sqrt{3}}\right|-\left(\frac{1}{2}\left(\sin\left(x\right)+\frac{1}{2}\right)\sqrt{\left(\sin\left(x\right)+\frac{1}{2}\right)^2+\frac{3}{4}}+\frac{3}{8}\ln\left|\frac{2\sqrt{\left(\sin\left(x\right)+\frac{1}{2}\right)^2+\frac{3}{4}}+2\sin\left(x\right)+1}{\sqrt{3}}\right|\right)$