# Lecture 2 Part 11 Integrals Class 12 Maths

**Logic for this lecture:**

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

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**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}-6log{(}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 *