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Question

Evaluate 1+xsinx+cosxx(1+cosx)dx

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Solution

1+xsinx+cosxx(1+cosx)dx

=1+cosxx(1+cosx)dx+xsinxx(1+cosx)dx

=1xdx+sinx1+cosxdx (It cos=θ


=logx+dtθ (sinxdx=dt)


=logxlogx+c

=logxlog(1+cosx)+c


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