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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 4 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 4 Maths Textbook Solution.

Answers (1)

Answer:

\frac{1}{3}(4 x+7)^{\frac{2}{3}}-\frac{1}{2} \sqrt{4 x+7}+c

Given:

\int\left(\frac{(8 x+13)}{\sqrt{4 x+7}} d x\right.

Hint:

Separate the terms and integrate

Solution:   

\int \frac{(8 x+13)}{\sqrt{4 x+7}} d x

    =\int \frac{8 x+14-1}{\sqrt{4 x+7}} d x

   =\int \frac{2(4 x+7)-1}{\sqrt{4 x+7}} d x

=\int \frac{2(4 x+7)}{\sqrt{4 x+7}}-\frac{1}{\sqrt{4 x+7}} d x

 \begin{aligned} &=2 \int \sqrt{4 x+7} d x-\int(4 x+7)^{\frac{1}{2}} d x \\ &=\frac{2\left((4 x+7)^{\frac{3}{2}}\right)}{4 \times \frac{3}{2}}-2 \frac{(4 x+7)^{\frac{1}{2}}}{4}+c \\ &=\frac{\left((4 x+7)^{\frac{3}{2}}\right)}{3}-\frac{(4 x+7)^{\frac{1}{2}}}{2}+c \end{aligned}

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