$\smallint 32\,\,{x^3}{\left( {\log \,\,x} \right)^2}dx$ is equal to

$8\,{x^4}\,\,{\left( {\log \,\,x} \right)^2} + \,\,c$

${x^4}\,\,\left\{ {\,8{{\left( {\log \,\,x} \right)}^2} - 4\,\,\log \,\,x\,} \right\} + c$

${x^3}\,\,\left\{ {\,{{\left( {\log \,\,x} \right)}^2} - 2\,\log \,\,x\,} \right\} + c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int 32\,\,{x^3}{\left( {\log \,\,x} \right)^2}dx

is equal to

View answer and explanation

Correct option: B

{x^4}\,\,\left\{ {\,8{{\left( {\log \,\,x} \right)}^2} - \,4\,\,\log \,\,x + 1\,} \right\} + c

Option B (

{x^4}\,\,\{\,8{{\left( {\log \,x} \right)}^2} - \,4\,\,\log \,x + 1\,\} + c

) is correct because it is the result of applying integration by parts twice to the given integral.