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Find the value of the intregral \int (ae)^{x}dx.

  • Option 1)

    \frac{(ae)^x}{\log a} +c

  • Option 2)

    \frac{(ae)^x}{1+\log a} +c

  • Option 3)

    (ae)^x +c

  • Option 4)

    (ae)^{x} \times \log a + c

 

Answers (1)

best_answer

As wehave learnt,

 

Indefinite integrals for Exponential functions -

\frac{\mathrm{d} }{\mathrm{d} x}\left ( e^{x} \right )=e^{x}

\int e^{x}dx=e^{x}+c

 

- wherein

\because \int a^{x}dx=\frac{a^{x}}{log_{e}a}

 

 \int (ae)^{x}dx = \frac{(ae)^{x}}{\log (ae)} + c =\frac{(ae)^{x}}{1 + \log (a)} + c

 


Option 1)

\frac{(ae)^x}{\log a} +c

Option 2)

\frac{(ae)^x}{1+\log a} +c

Option 3)

(ae)^x +c

Option 4)

(ae)^{x} \times \log a + c

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gaurav

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