Use the reduction formula: [(In 2)" dx = 2(In x)" — n f (In 2)¹-1, times. First application of the reduction formula (n = 3): f(In x)³ dx =+Sdx. Second application of the reduction formula (n = 2): S(In x)³ dx = + Sdx. Third application of the reduction formula: (n = 1) (In)³dx=+S dx. Wrap-up: So completing the final integration above, S(In z)³dx=+C. "¹dx to evaluate f(lnx) ³dx. To achieve this, you will need to apply the reduction formula 3

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Use the reduction formula: [(In 2)" dx = x(ln z)" — n f (In 2)¹-1,
times.
First application of the reduction formula (n = 3):
f(In x)³ dx =+Sdx.
Second application of the reduction formula (n = 2):
(In z) ³dx=+ dr.
Third application of the reduction formula: (n = 1)
(In x) ³dx=+ dx.
Wrap-up: So completing the final integration above,
S(In z)³ dx=+C.
"1¹dx to evaluate f(lnx) ³dx. To achieve this, you will need to apply the reduction formula 3
Transcribed Image Text:Use the reduction formula: [(In 2)" dx = x(ln z)" — n f (In 2)¹-1, times. First application of the reduction formula (n = 3): f(In x)³ dx =+Sdx. Second application of the reduction formula (n = 2): (In z) ³dx=+ dr. Third application of the reduction formula: (n = 1) (In x) ³dx=+ dx. Wrap-up: So completing the final integration above, S(In z)³ dx=+C. "1¹dx to evaluate f(lnx) ³dx. To achieve this, you will need to apply the reduction formula 3
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