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\int { \frac { { \left( x+3 \right) e }^{ x } }{ (x+5)^{ 3 } } dx }

Note by Abhay Raj Singh 2 years, 2 months ago

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\( \int { \frac { { \left( x+3 \right) e }^{ x } }{ (x+5)^{ 3 } } dx } \)

\( = \int \frac { ( x+5 - 2) e^x }{ (x+5)^3 } dx \)

\( = \int \frac { (x+5) e^x }{ (x+5)^3 } dx + \int \frac { - 2 e^x }{ (x+5)^3 } dx \)

\( = \int \frac { e^x }{ (x+5)^2 } dx + \int \frac { - 2 e^x }{ (x+5)^3 } dx \)

Using IBP on the second integral with\( u = e^x \) and \( dv = \frac{- 2}{(x+5)^3} \)

\( = \int \frac { e^x }{ (x+5)^2 } dx + \frac{e^x}{(x+5)^2} -\int \frac { e^x }{ (x+5)^2 } dx \)

\( = \frac{e^x}{(x+5)^2} \) – Siddhartha Srivastava · 2 years, 2 months ago

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@Siddhartha Srivastava – thanx – Abhay Raj Singh · 2 years, 2 months ago

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TopNewest\( \int { \frac { { \left( x+3 \right) e }^{ x } }{ (x+5)^{ 3 } } dx } \)

\( = \int \frac { ( x+5 - 2) e^x }{ (x+5)^3 } dx \)

\( = \int \frac { (x+5) e^x }{ (x+5)^3 } dx + \int \frac { - 2 e^x }{ (x+5)^3 } dx \)

\( = \int \frac { e^x }{ (x+5)^2 } dx + \int \frac { - 2 e^x }{ (x+5)^3 } dx \)

Using IBP on the second integral with\( u = e^x \) and \( dv = \frac{- 2}{(x+5)^3} \)

\( = \int \frac { e^x }{ (x+5)^2 } dx + \frac{e^x}{(x+5)^2} -\int \frac { e^x }{ (x+5)^2 } dx \)

\( = \frac{e^x}{(x+5)^2} \) – Siddhartha Srivastava · 2 years, 2 months ago

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– Abhay Raj Singh · 2 years, 2 months ago

thanxLog in to reply