Explanation Given: The provided integral formula is ∫ u n a + b u d u = 2 ( 2 n + 1 ) b ( u n a + b u − n a ∫ u n − 1 a + b u d u ) . Formula used: The formula used is integration by parts, u and v are two terms ∫ u ⋅ v = u ∫ v − ∫ ( ∫ v ) u ′ Proof: Taking the left-hand side, ∫ u n a + b u d u In this w = u n , v = 1 a + b u , the integral is solved as ∫ u n a + b u d u = u n ∫ [ d u a + b u − ∫ [ ( ∫ d u a + b u d u ) ⋅ d d x ( u n ) d u ] ] = 2 u n b a + b u − 2 n b ∫ u n − 1 a + b u d u = 2 u n b a + b u − 2 n b <

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Chapter 8.7, Problem 50E

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To prove: The integral formula ∫una+budu=2(2n+1)b(una+bu−na∫un−1a+budu).

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Chapter 8.7, Problem 49E

Chapter 8.7, Problem 51E

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Chapter 8 Solutions

CALCULUS: EARLY TRANSCENDENTAL FUNCTIO

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To prove: The integral formula ∫ u n a + b u d u = 2 ( 2 n + 1 ) b ( u n a + b u − n a ∫ u n − 1 a + b u d u ) .

Solution Summary: The author explains the integral formula, which is integrated by parts, u and v are two terms.

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To prove: The integral formula ∫una+budu=2(2n+1)b(una+bu−na∫un−1a+budu).

Want to see the full answer?

Chapter 8 Solutions