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Evaluate abcd∫3axb2+c2x2dx

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Question

Evaluate `int (3"a"x)/("b"^2 + "c"^2x^2) "d"x`

Sum

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Solution

Let v = b² + c2x², then dv = 2c² xdx

Therefore, `int (3"a"x)/("b"^2 + "c"^2x^2) "d"x`

= `(3"a")/(2"c"^2) int "dv"/"v"`

= `(3"a")/("c"^2) log |"b"^2 + "c"^2x^2| + "C"`

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Definite Integrals

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Chapter 7: Integrals - Solved Examples [Page 147]

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NCERT Exemplar Mathematics Exemplar [English] Class 12

Chapter 7 Integrals
Solved Examples | Q 2 | Page 147

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