If $$J=$$∫$$e2x+aexdx$$ then J is equal to

Correct option is 1e2x+aex+alogex2+ex+a+C

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$If J = \int \sqrt{e^{2 x} + a e^{x}} d x then J is equal to$

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e2x+aex+alogex2+ex+a+C

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detailed solution

Correct option is A

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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If J=∫e2x+aexdx then J is equal to

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$If J = \int \sqrt{e^{2 x} + a e^{x}} d x then J is equal to$