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Question

1x13(x61)dx

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Solution

We have,

1x13(x61)dx

On multiplying and dividing x5

Then,

x5x18(x61)dx

x5(x6)3(x61)dx

Let,

t=x6

dt=6x5dx

15dt=x5dx

Now,

16t3(t1)dt

By application of partial dfraction

Then,

16t3(t1)dt=16(t1)dy16tdy16t2dy16t3dy

16t3(t1)dt=16log(t1)16logt+16t+112t2

Substitution of t, gives us

1x13(x61)dx=16log(x61)16logx6+16x6+112x12

Hence, this is the answer.

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