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Question

x(1+x2)3/2dx=

A
11+x2+c
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B
1(1+x2)+c
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C
1(1+x2)3/2+c
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D
1(1+x2)+c
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Solution

The correct option is A 11+x2+c
I=x(1+x2)3/2dx

x2=t
2xdx=dt
xdx=12dt
Then,
I=12dt(1+t)3/2=12dt(1+t)3/2
=1/2(2)(1+t)1/2+c
=1(1+t)1/2+c
=11+x2+c(t=x2)
x(1+x2)3/2=11+x2+c

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