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  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 26

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 26

Answers (1)

Answer:  \frac{\log\left | 3+a^{x} \right |}{\ln \left ( a \right )}+c

Hints: You must know about the integral rules of x

Given: \int \frac{a^{x}}{3+a^{x}}dx

Solution:

I=\int \frac{a^{x}}{3+a^{x}}dx

Lett= 3+ a^{x}.         and differentiate both sides

d t=0+a^{x} \ln (a) d x \quad\quad \quad \quad \quad \quad \quad \quad{\left[\frac{d}{d x} a^{x}=a^{x} \ln |a|\right]} \\

I=\int \frac{d t}{\ln (a) t} \quad \quad \quad \quad \quad \quad \quad \quad {\left[\int \frac{1}{x} d x=\log x+c\right]}

 \begin{aligned} &=\frac{1}{\ln a} \int \frac{d t}{t} \\ &=\frac{1}{\ln a} \log |t|+c \\ &=\frac{\log \left|3+a^{x}\right|}{\ln (a)}+c \end{aligned}

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