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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 90 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 90 Maths Textbook Solution.

Answers (1)

Answer:

\frac{\left(4 x^{2}+5 x+6\right)^{\frac{3}{2}}}{6}+\frac{7}{8} \int \frac{x}{2} \sqrt{4 x^{2}+5 x+6}-\frac{1}{8} \ln \left|2 x+\sqrt{4 x^{2}+5 x+6}\right|+c

Hint:

You must have to know about integration method.

Given:

\int(2 x+3) \sqrt{4 x^{2}+5 x+6} d x

Solution:

\int(2 x+3) \sqrt{4 x^{2}+5 x+6} d x

\frac{1}{4} \int(8 x+5+7) \sqrt{4 x^{2}+5 x+6} d x

\frac{1}{4} \int(8 x+5) \sqrt{4 x^{2}+5 x+6} d x+7 \int \sqrt{4 x^{2}+5 x+6} d x

\text { Let } 4 x^{2}+5 x+6=t

\frac{\frac{1}{4}\left(t^{\frac{1}{2}}+1\right)}{\frac{3}{2}}+7 \int \sqrt{\left(2 x+\frac{5}{2}\right)^{2}}+\left(6-\frac{25}{4}\right) d x

\frac{1}{4}\left(\frac{2\left(\sqrt{4 x^{2}+5 x+6}\right)}{3} \cdot\left(4 x^{2}+5 x+6\right)+7 \int \sqrt{\left(2 x+\frac{5}{2}\right)^{2}}+\frac{1}{4} d x\right.

\int \frac{\left(4 x^{2}+5 x+6\right)^{\frac{3}{2}}}{6}+\frac{7}{4} \sqrt{\left(2 x+\frac{5}{2}\right)^{2}}+\left(\frac{1}{2}\right)^{2} d x

\int \frac{\left(4 x^{2}+5 x+6\right)^{\frac{3}{2}}}{6}+\frac{7}{4} \sqrt{\left(2 x+\frac{5}{2}\right)^{2}}+\left(\frac{1}{2}\right)^{2} d x

\frac{\left(4 x^{2}+5 x+6\right)^{\frac{3}{2}}}{6}+\frac{7}{4} \sqrt{\left(2 x+\frac{5}{2}\right)^{2}\left(-\frac{1}{2}\right)^{2}}-\frac{1}{4} \times \frac{1}{2} \ln \left|2 x+\sqrt{4 x^{2}+5 x+6}\right|+c

\frac{\left(4 x^{2}+5 x+6\right)^{\frac{3}{2}}}{6}+\frac{7}{8} \int \frac{x}{2} \sqrt{4 x^{2}+5 x+6}-\frac{1}{8} \ln \left|2 x+\sqrt{4 x^{2}+5 x+6}\right|+c

 

Posted by

infoexpert21

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