Explanation Formula used: ∫ u ( a + b u ) 2 ( c + d u ) d u = − a b ( a d − b c ) 1 a + b u − c ( a d − b c ) 2 ln | c + d u a + b u | Calculation: The given integral is ∫ x ( 5 + 2 x ) 2 ( 2 + x ) d x . Let ( a + b u ) 2 = ( 5 + 2 x ) 2 and ( c + d u ) = ( 2 + x ) . Then the integral can be rewritten as follows. ∫ x ( 5 + 2 x ) 2 ( 2 + x ) d x = ∫ u ( 5 + 2 u ) 2 ( 2 + u ) d u The integral ∫ u ( 5 + 2 u ) 2 ( 2 + u ) d u is similar to ∫ u ( a + b u ) 2 ( c + d u ) d u , where a = 5 , b = 2 , c = 2 , d = 1 , u = x

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Chapter 6.4, Problem 12E

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To evaluate: The given indefinite integral ∫x(5+2x)2(2+x)dx.

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Chapter 6.4, Problem 11E

Chapter 6.4, Problem 13E

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The given indefinite integral ∫ x ( 5 + 2 x ) 2 ( 2 + x ) d x .

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To evaluate: The given indefinite integral ∫x(5+2x)2(2+x)dx.

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