NCERT Class 12 Maths
Chapter 7: Integrals
23 Questions Solved
NCERT Solutions for Class 12 Maths Chapter 7 Integrals — Exercise 7.5
Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.
Question 1
Evaluate \(\int \frac{x}{\left(x + 1\right) \left(x + 2\right)}\, dx\).
Question 2
Evaluate \(\int \frac{1}{x^{2} - 9}\, dx\).
Question 3
Evaluate \(\int \frac{3 x - 1}{\left(x - 3\right) \left(x - 2\right) \left(x - 1\right)}\, dx\).
Question 4
Evaluate \(\int \frac{x}{\left(x - 3\right) \left(x - 2\right) \left(x - 1\right)}\, dx\).
Question 5
Evaluate \(\int \frac{2 x}{x^{2} + 3 x + 2}\, dx\).
Question 6
Evaluate \(\int \frac{1 - x^{2}}{x \left(1 - 2 x\right)}\, dx\).
Question 7
Evaluate \(\int \frac{x}{\left(x - 1\right) \left(x^{2} + 1\right)}\, dx\).
Question 8
Evaluate \(\int \frac{x}{\left(x - 1\right)^{2} \left(x + 2\right)}\, dx\).
Question 9
Evaluate \(\int \frac{3 x + 5}{x^{3} - x^{2} - x + 1}\, dx\).
Question 10
Evaluate \(\int \frac{2 x - 3}{\left(2 x + 3\right) \left(x^{2} - 1\right)}\, dx\).
Question 11
Evaluate \(\int \frac{5 x}{\left(x + 1\right) \left(x^{2} - 4\right)}\, dx\).
Question 12
Evaluate \(\int \frac{x^{3} + x + 1}{x^{2} - 1}\, dx\).
Question 13
Evaluate \(\int \frac{2}{\left(1 - x\right) \left(x^{2} + 1\right)}\, dx\).
Question 14
Evaluate \(\int \frac{3 x - 1}{\left(x + 2\right)^{2}}\, dx\).
Question 15
Evaluate \(\int \frac{1}{x^{4} - 1}\, dx\).
Question 16
Evaluate \(\int \frac{1}{x \left(x^{n} + 1\right)}\, dx\).
Question 17
Evaluate \(\int \frac{\cos{\left(x \right)}}{\left(1 - \sin{\left(x \right)}\right) \left(2 - \sin{\left(x \right)}\right)}\, dx\).
Question 18
Evaluate \(\int \frac{\left(x^{2} + 1\right) \left(x^{2} + 2\right)}{\left(x^{2} + 3\right) \left(x^{2} + 4\right)}\, dx\).
Question 19
Evaluate \(\int \frac{2 x}{\left(x^{2} + 1\right) \left(x^{2} + 3\right)}\, dx\).
Question 20
Evaluate \(\int \frac{1}{x \left(x^{4} - 1\right)}\, dx\).
Question 21
Evaluate \(\int \frac{1}{e^{x} - 1}\, dx\).
Question 22
Evaluate \(\int \frac{x}{\left(x - 2\right) \left(x - 1\right)}\, dx\).
Question 23
Evaluate \(\int \frac{1}{x \left(x^{2} + 1\right)}\, dx\).