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Q.

If J=∫e2x+aexdx then J is equal to

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a

e2x+aex+alogex2+ex+a+C

b

e2x+aex+alogex+ae2x+C

c

e2x+aex+alogex2+eax+C

d

e2x+aex+logex+ex+a+C

answer is A.

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Detailed Solution

J=∫ex1+ae−x dx Put ex=t2exdx=2tdtJ=∫2t1+at2dtJ=2∫t2+adt=2t2t2+a+a2log⁡t+t2+a+CJ=e2x+aex+alog⁡ex2+ex+a+C
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