RD Sharma Class 12 Solutions Indefinite Integrals Ex 18.29 examining material is one of the most staggering course books for class 12 maths explicitly for students planning simple tests. The RD Sharma solutions meets an incredible essential of maths questions. Rd Sharma Class 12th exercise 18.29 is an accomplishment for every understudy. One book that has been given to students for rehearsing and tackling for Rd Sharma Class 12th exercise 18.29.
Chapter 18 - Indefinite Integrals - Ex-18.1
Indefinite Integrals Exercise 18.29 Question 1
Answer : $-\frac{1}{3}\left(x^{2}-x+1\right)^{\frac{3}{2}}+\frac{3}{8}\left(2 x-1 \sqrt{x^{2}-x+1}+3 \ln \left|x+\frac{1}{2}+\sqrt{x^{2}-x+1}\right|+C\right.$Indefinite Integrals Exercise 18.29 Question 2
Answer : $\frac{1}{6}\left(2 x^{2}+3\right)^{\frac{3}{2}}+\frac{x}{2} \sqrt{x^{2}-x+1}+\frac{3 \sqrt{2}}{4} \log \left|\frac{\sqrt{2 x}+\sqrt{2 x^{2}+3}}{\sqrt{3}}\right|+C$Indefinite Integrals Exercise 18.29 Question 3
Answer :Indefinite Integrals Exercise 18.29 Question 4
Answer : $\\\frac{1}{3}\left(x^{2}+x+1\right)^{\frac{3}{2}}+\frac{3(2 x+1)}{8} \sqrt{x^{2}+x+1}+\frac{9}{16} \log \left|\left(x+\frac{1}{2}\right)+\sqrt{x^{2}+x+1}\right|+C$Indefinite Integrals Exercise 18.29 Question 5
Answer: $\\\frac{4}{3}\left(x^{2}+x+1\right)^{\frac{3}{2}}+\frac{3(2 x+1)}{8} \sqrt{x^{2}+x+1}+\frac{27}{8} \log \left|\left(x+\frac{1}{2}\right)+\sqrt{x^{2}+x+1}\right|+C$Indefinite Integrals Exercise 18.29 Question 6
Answer : $\\I=\frac{1}{6}\left(2 x^{2}-6 x+5\right)^{3 / 2}-\frac{1}{2}\left[\frac{2 x-3}{2} \sqrt{x^{2}-3 x+\frac{5}{2}}+\frac{11}{8} \log \left|\frac{2 x-3}{\sqrt{2}}+\sqrt{2 x^{2}-6 x+5}\right|\right]+C$Indefinite Integrals Exercise 18.29 Question 7
Answer : $\\I=\frac{\left(x^{2}+x+1\right)}{2}+\frac{1}{2}\left[\frac{2 x+1}{4} \sqrt{x^{2}+x+1}+\frac{3}{8} \log \left|\left(x+\frac{1}{2}\right)+\sqrt{x^{2}+x+1}\right|\right]+C$Indefinite Integrals Exercise 18.29 Question 8
Answer : $\\I=\frac{2}{3}\left(x^{2}+4 x+3\right)^{3 / 2}-\frac{(x+2)}{2} \sqrt{x^{2}+4 x+3}+\frac{1}{2} \log \left|(x+2)+\sqrt{x^{2}+4 x+3}\right|+C$Indefinite Integrals Exercise 18.29 Question 9
Answer : $\\I=\frac{2}{3}\left(x^{2}-4 x+3\right)^{3 / 2}-\frac{(x-2)}{2} \sqrt{x^{2}-4 x+3}-\frac{1}{2} \log \left|(x-2)+\sqrt{x^{2}-4 x+3}\right|+C$Indefinite Integrals Exercise 18.29 Question 10
Answer : $I=\frac{1}{3}\left(x^{2}+x\right)^{3 / 2}-\frac{1}{8}(2 x+1) \sqrt{x^{2}+x}+\frac{1}{16} \log \left|\left(x+\frac{1}{2}\right)+\sqrt{x^{2}+x}\right|+C$Indefinite Integrals Exercise 18.29 Question 11
Answer : $\\I=\frac{1}{3}(x+3 x-18)^{3 / 2}-\frac{9}{8}(2 x+3) \sqrt{x^{2}+3 x-18}+\frac{729}{16} \log \left|\left(x+\frac{3}{2}\right)+\sqrt{x^{2}+3 x-18}\right|+C$Indefinite Integrals Exercise 18.29 Question 12
Answer : $I=-\frac{1}{3}\left(3-4 x-x^{2}\right)^{\frac{3}{2}}+\frac{1}{2}(x+2) \sqrt{3-4 x-x^{2}}+\frac{7}{2} \sin ^{-1}\left(\frac{x+2}{\sqrt{7}}\right)+C$Indefinite Integrals Exercise 18.29 Question 13
Answer : $I=-\frac{1}{2}\left(4-3 x-2 x^{2}\right)^{\frac{3}{2}}-\frac{5}{4}\left(\frac{2 x+3}{2 \sqrt{2}} \sqrt{4-3 x-2 x^{2}}+\frac{17}{4} \sin ^{-1} \frac{(2 x+3)}{\sqrt{17}}\right)+C$Indefinite Integrals Exercise 18.29 Question 14
Answer : $\frac{-2}{9}\left(10-4 x-3 x^{2}\right)^{\frac{3}{2}}+\frac{11}{8}(3 x+2) \sqrt{10-4 x+3 x^{2}}+\frac{187}{9 \sqrt{3}} \sin ^{-1}\left(\frac{3 x+2}{\sqrt{34}}\right)+C$Rd Sharma class 12 chapter 18 exercise 18.29 has around 14 inquiries, including its subparts, and it consolidates themes like: -
Assessment of integrals by utilizing mathematical replacements like first need to solve the quadratic equation then proceed with the differentiation and integration
Questions based on the Formula of Integration
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