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  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefiite Integrals Excercise Fill in the Blanks Question 6

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefiite Integrals Excercise Fill in the Blanks Question 6

Answers (1)

Answer:

\frac{e^{x}}{x+4}+c

Hint:

Simplify the function and then integrate it.

Solution:

\begin{aligned} &I=\int \frac{x+3}{(x+4)^{2}} e^{x} d x \\ &I=\int \frac{x+4-1}{(x+4)^{2}} e^{x} d x \\ &I=I=\int\left[\frac{1}{x+4}-\frac{1}{(x+4)^{2}}\right] e^{x} d x \end{aligned}

 

Let  f(x)=\frac{1}{x+4}

 

then  {f}'\left (x \right )=-\frac{1}{\left ( x+4 \right )^{2}}

\begin{aligned} &\Rightarrow I=\int\left[f(x)+f^{\prime}(x)\right] e^{x} d x \\ &\Rightarrow I= \int\left[f(x)+f^{\prime}(x)\right] e^{x} d x \\ &\Rightarrow I=f(x) e^{x}+c \\ &I=\frac{e^{x}}{x+4}+c \end{aligned}

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