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Question

Evaluate:dt16+6sint

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Solution

dt16+6sint
=12dt8+3sint
Let sint=1tan2t21+tan2t2
=121+tan2t28+8tan2t2+33tan2t2dt
=12sec2t28+8tan2t2+33tan2t2dt
Let u=tant2du=12sec2t2dt
2du=sec2t2dt
=122du11+5u2
=122du15((55)2+u2)
=555tan1(u55)+c where c is the constant of integration.
=555tan1⎜ ⎜tant255⎟ ⎟+c where u=tant2

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