Expand the integral $\int\left(\tan\left(x\right)-\sin\left(2x\right)\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately
The integral $\int\tan\left(x\right)dx$ results in: $-\ln\left(\cos\left(x\right)\right)$
The integral $\int-\sin\left(2x\right)dx$ results in: $\frac{1}{2}\cos\left(2x\right)$
Gather the results of all integrals
As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$
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