# Lecture 2 Part 10 Integrals Class 12 Maths

**Logic for this lecture:**

**Second way****:** in case of all linear variables in question, you can substitute bigger linear expression of question and find the value for smaller linear expression from that. You can also use this method in case of exponential functions. *You can also use division if there is no root in function and it is an improper fraction.*

**Questions Discussed in this lecture:**

*Q74. \int{\frac{x}{\sqrt{x+4}}dx=\frac{2}{3}\sqrt{x+4}(x-8)+C} *

*Q75. \int{\frac{2x-1}{2x+3}dx} = x-log{|}(2x+3)^2|+C *

*Q76. \int{\frac{8x+13}{\sqrt{4x+7}}dx} = \frac{1}{3}(4x+7)^\frac{3}{2}-\frac{1}{2}(4x+7)^\frac{1}{2}+C *

*Q77. \int{\frac{x}{\sqrt{x+2}}dx} = \frac{2}{3}(x+2)^\frac{3}{2}-4(x+1)^\frac{1}{2}+C *

*Q78. \int{\frac{x+1}{\sqrt{2x-1}}dx}=\frac{1}{6}(2x-1)^\frac{3}{2}+\frac{3}{2}(2x-1)^\frac{1}{2}+C *