# Lecture 2 Part 11 Integrals Class 12 Maths

## Part - 11 Lecture - 2 Chapter 7 Integrals

Sometimes we’re tested not to show our weaknesses, but to discover our strengths.

Booklets/Notes/Assignments are typed here on this website and their PDFs will be made available soon.

Logic for this lecture:

Third way: You can substitute any trigonometric or algebraic value.

Questions Discussed in this lecture:

Q79. $$\int\frac{x^5}{x+1}dx=\frac{x^5}{5}-\frac{x^4}{4}+\frac{x^3}{3}-\frac{x^2}{2}+x-\log{|}x+1|+C$$

Q80. $$\int{\frac{x^4+1}{x^2+1}dx=\frac{x^3}{3}-x+2{tan}^{-1}{x}+C}$$

Q81. $$\int{\frac{1}{x^\frac{1}{2}+x^\frac{1}{3}}dx=2\sqrt x-3x^\frac{1}{3}+6x^\frac{1}{6}-6\log{(}1+x^\frac{1}{6})+C}$$

Q82. $$\int\sqrt{\frac{1-\sqrt x}{1+\sqrt x}}dx=-2\sqrt{1-x}+{\cos}^{-1}{\sqrt x}+\sqrt{x-x^2}+C$$