# Lecture 2 Part 11 Integrals Class 12 Maths

## Part - 11 Lecture - 2 Chapter 7 Integrals

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

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

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