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NCERT Class 12 Maths Chapter 7: Integrals 25 Questions Solved

NCERT Solutions for Class 12 Maths Chapter 7 Integrals — Exercise 7.4

Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.

Evaluate \(\int \frac{3 x^{2}}{x^{6} + 1}\, dx\).

Evaluate \(\int \frac{1}{\sqrt{4 x^{2} + 1}}\, dx\).

Evaluate \(\int \frac{1}{\sqrt{\left(2 - x\right)^{2} + 1}}\, dx\).

Evaluate \(\int \frac{1}{\sqrt{9 - 25 x^{2}}}\, dx\).

Evaluate \(\int \frac{3 x}{2 x^{4} + 1}\, dx\).

Evaluate \(\int \frac{x^{2}}{1 - x^{6}}\, dx\).

Evaluate \(\int \frac{x - 1}{\sqrt{x^{2} - 1}}\, dx\).

Evaluate \(\int \frac{x^{2}}{\sqrt{a^{6} + x^{6}}}\, dx\).

Evaluate \(\int \frac{\sec^{2}{\left(x \right)}}{\sqrt{\tan^{2}{\left(x \right)} + 4}}\, dx\).

Evaluate \(\int \frac{1}{\sqrt{x^{2} + 2 x + 2}}\, dx\).

Evaluate \(\int \frac{1}{9 x^{2} + 6 x + 5}\, dx\).

Evaluate \(\int \frac{1}{\sqrt{- x^{2} - 6 x + 7}}\, dx\).

Evaluate \(\int \frac{1}{\sqrt{\left(x - 2\right) \left(x - 1\right)}}\, dx\).

Evaluate \(\int \frac{1}{- x^{2} + 3 x + 8}\, dx\).

Evaluate \(\int \frac{1}{\sqrt{\left(- a + x\right) \left(- b + x\right)}}\, dx\).

Evaluate \(\int \frac{4 x + 1}{\sqrt{2 x^{2} + x - 3}}\, dx\).

Evaluate \(\int \frac{x + 2}{\sqrt{x^{2} - 1}}\, dx\).

Evaluate \(\int \frac{5 x - 2}{3 x^{2} + 2 x + 1}\, dx\).

Evaluate \(\int \frac{6 x + 7}{\sqrt{\left(x - 5\right) \left(x - 4\right)}}\, dx\).

Evaluate \(\int \frac{x + 2}{\sqrt{- x^{2} + 4 x}}\, dx\).

Evaluate \(\int \frac{x + 2}{\sqrt{x^{2} + 2 x + 3}}\, dx\).

Evaluate \(\int \frac{x + 3}{x^{2} - 2 x - 5}\, dx\).

Evaluate \(\int \frac{5 x + 3}{\sqrt{x^{2} + 4 x + 10}}\, dx\).

Evaluate \(\int \frac{1}{x^{2} + 2 x + 2}\, dx\).

Evaluate \(\int \frac{1}{\sqrt{- 4 x^{2} + 9 x}}\, dx\).