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Grade 12th passIntegral Calculus

evaluate ∫ a^xe^x with respect to x
options
A . (ae)^x
B. ( a^xe^x)/loga +logx
C.(ae)^x/1+loga
D.(ae)^x/logax

rangu meghana

9 Years agoGrade 12th pass

1 Answer

Ritika Das

9 Years ago

Let u=a^xe^x

du/dx=e^xa^xloga+a^xe^x

=e^xa^x(loga+1)

Therefore, dx=du/{e^xa^x(loga+1)}

So, ∫a^xe^x.dx = ∫a^xe^x.du/{e^xa^x(loga+1)}.......[putting value of dx from above in here]

Answer is option C.

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