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Question

Evaluate:
1(2x7)(x3)(x4) dx

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Solution

I=dx(2x7)(x3)(x4)

=(x3)(x4)(2x7)dx

=x23x4x+122x7dx

=x27x+122x7dx

=x22.72x+(72)2(72)2+122x7dx

=(x72)2+124942x7dx

=(x72)2(12)22(172)dx

Let (x72)2(12)2=t2
2(x72)dx=2tdt dx=2tdt2(x72)

I=t.tdt2(x72)2

=14t2dt(x72)2

=14t2+1414dtt2+14

=141dt141t2+14dt

=14t14×14tan1t14+c

=14ttan1t14+c
=14x27x+12tan14(x3)(x4)+c
Hence, the answer is 14x27x+12tan14(x3)(x4)+c.

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