# Part - 10 Lecture - 2 Chapter 7 Integrals

It’s going to be hard, but hard does not mean impossible.

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

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