Evaluate ∫(cosx-sinx)dx
12logtanx2–π8+c
12logcotx2+c
12logcotx2–3π8+c
12logtanx2+3π8+c
Explanation for the correct option
Integrating the given integral
Given, ∫(cosx-sinx)dx
Solving the integral,
∫(cosx-sinx)dx=12∫dx12cosx−12sinx=12∫dxcosπ4.cosx-sinπ4.sinx=12∫dxcosx+π4∵cos(a+b)=cos.cosb-sina.sinb=12∫secx+π4dx=12logtanπ4+x2+π8+C=12logtanx2+3π8+C
Hence, the correct answer is Option (D).