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Question

Integrate
3+4sinx+2cosx3+2sinx+cosxdx

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Solution

2x3dtt2+2×14x+116+2+c

=2x3dt(t+14)2+3116+c

=2x3dt(t+14)2+(314)2+c

=2x31314tan1t+14314+c

=2x1231tan1tan14t+131+c

=2x1231tan1⎜ ⎜4tanx2+131⎟ ⎟+c
Hence, the answer is 2x1231tan1⎜ ⎜4tanx2+131⎟ ⎟+c.

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