If ${I_n} = \smallint \,\,{x^n}\,.\,\,{e^{cx}}\;\,dx\;\;\,{\rm{for}}\,\;\;n\,\, \ge \,\,1,\,\;{\rm{then}}\,\,c\,.\,{I_n}\,\, + \,\,n\,.\,{I_{n - 1}}$ is equal to

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

{I_n} = \int \,\,{x^n}\,.\,\,{e^{cx}}\;\,dx\;\;\,\mathrm{for}\,\;\;n\,\, \ge \,\,1,\,\;\mathrm{then}\,\,c\,.\,{I_n}\,\, + \,\,n\,.\,{I_{n - 1}}

is equal to

View answer and explanation

Correct option: A

{x^n}\,{e^{cx}}

Option A (

{x^n}\,{e^{cx}}

) is correct because integrating by parts and rearranging the terms leads to the given expression.