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Question

Evaluate: 3x24+5x6dx

A
1(5)tan15x32.
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B
12(5)tan13x32.
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C
12(5)tan15x52.
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D
12(5)tan15x32.
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Solution

The correct option is C 12(5)tan15x32.
Let I=3x24+5x6dx
Let u=x3
dudx=3x2
du=3x2dx

I=du4+5u2
Now, apply integral substitution,
u=25v

I=dv25(v2+1)dv

I=1251v2+1dv

I=125tan1v

I=125tan1(52u) [ Re-substituting value of v ]

I=125tan1(52x3) [ Re-substituting value of u ]

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