Karnataka Board PUCPUC Science 2nd PUC Class 12

Write a Value of ∫ a X 3 + a X D X - Mathematics

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Sum

Write a value of

\[\int\frac{a^x}{3 + a^x} \text{ dx}\]
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Solution

\[\text{ Let I }= \int \frac{a^x dx}{3 + a^x}\]
\[\text{ Let 3} + a^x = t\]
\[ \Rightarrow a^x . \text{ log  a  dx }= dt\]
\[ \Rightarrow a^x dx = \frac{dt}{\log a}\]
\[ \therefore I = \frac{1}{\log a}\int\frac{dt}{t}\]
\[ = \frac{1}{\log a}\log t + C\]
\[ = \frac{1}{\log a}\log   \left( \text{ 3 }+ a^x \right) + C\left( \because t=3 + a^x \right)\]

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Chapter 19: Indefinite Integrals - Very Short Answers [Page 197]

APPEARS IN

RD Sharma Class 12 Maths
Chapter 19 Indefinite Integrals
Very Short Answers | Q 26 | Page 197

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