The value of $\smallint {e^{2x}}\,(2\,\,\sin \,\,3x\,\, + \,\,3\,\,\cos \,\,3x)\,dx$ is

${e^{2x}}\,\,\cos \,\,3x\,\, + \,\,c$

${e^{2x}}\;(2\,\,\sin \,\,3x)\,\, + \,\,c$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Analyzing +4 | -1

The value of

\int {e^{2x}}\,(2\,\,\sin \,\,3x\,\, + \,\,3\,\,\cos \,\,3x)\,dx

View answer and explanation

Correct option: A

{e^{2x}}\,\,\sin \,\,3x\,\, + \,\,c

Option A (

{e^{2x}}\sin \\,3x\\, + \\,c

) is correct because the integral can be solved by recognizing a pattern where the cosine term cancels out after integration by parts.

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