I=∫(log⁡2((sin⁡([x]π)x2+x+1)+sgn⁡(x2+x+1)+1)) dxI=\int \left(\log_2\left(\left(\frac{\sin([x]\pi)}{x^2+x+1}\right)+\operatorname{sgn}(x^2+x+1)+1\right)\right)\,dx…

Mathematics

Problem

I=∫(log⁡2((sin⁡([x]π)x2+x+1)+sgn⁡(x2+x+1)+1)) dxI=\int \left(\log_2\left(\left(\frac{\sin([x]\pi)}{x^2+x+1}\right)+\operatorname{sgn}(x^2+x+1)+1\right)\right)\,dx is equal to (where [⋅][\cdot] and sgn⁡(⋅)\operatorname{sgn}(\cdot) denotes greatest integer function and signum function respectively) (a) x+Cx+C (b) cos⁡x+x+C\cos x+x+C (c) sin⁡x+sgn⁡(x2+x+1)+x+C\sin x+\operatorname{sgn}(x^2+x+1)+x+C (d) −x+C-x+C (a) x+Cx+C (b) cos⁡x+x+C\cos x+x+C (c) sin⁡x+sgn⁡(x2+x+1)+x+C\sin x+\operatorname{sgn}(x^2+x+1)+x+C (d) −x+C-x+C

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