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Logics for this lecture:

Question must be in addition/subtraction form.

Try to convert division/multiplication between functions to addition/subtraction by simplification.

If there are functions other than algebraic functions like trigonometry and logarithmic function, then you can use their respective identities to simplify them.

Logics for this lecture:

Question must be in addition/subtraction form.

Try to convert division/multiplication between functions to addition/subtraction by simplification.

If there are functions other than algebraic functions like trigonometry and logarithmic function, then you can use their respective identities to simplify them.

Questions Discussed in this lecture:
1. $$\int x^{2} \left(1-\frac{1}{x^{2} } \right), dx =\frac{x^{3} }{3} -x+C$$

2. $$\int _{}^{}\left(\sqrt{x} -\frac{1}{\sqrt{x} } \right) ^{2} dx=\frac{x^{2} }{2} +\log |x|-2x+C$$

3. $$\int \left(8^{x} +x^{8} +\frac{8}{x} +\frac{x}{8} \right), dx =\frac{8^{x} }{\log 8} +\frac{x^{9} }{9} +8\log |x|+\frac{x^{2} }{16} +C$$

4. $$\int (e^{a\log x} +e^{x\log a} ), dx =\frac{x^{a+1} }{a+1} +\frac{a^{x} }{\log a} +C$$

5. $$\int \left(\frac{\cos 2x+2\sin ^{2} x}{\cos ^{2} x} \right) , dx=\tan x+C$$

6. $$\int (x^{c} +c^{x} ), dx =\frac{x^{c+1} }{c+1} +\frac{c^{x} }{\log c} +C$$

7. $$\int _{}^{}\frac{x^{2} +3x+4}{\sqrt{x} } , dx=\frac{2}{5} x^{\frac{5}{2} } +2x^{\frac{3}{2} } +8\sqrt{x} +C$$

8. $$\int \left(\frac{2a}{\sqrt{x} } -\frac{b}{x^{2} } +3c, , \sqrt[{3}]{x^{2} } \right) , dx=4a\sqrt{x} +\frac{b}{x} +\frac{9cx^{\frac{5}{3} } }{5} +C$$

9. $$\int _{}^{}\frac{x^{3} -x^{2} +x-1}{x-1} , , dx =\frac{x^{3} }{3} +x+C$$

10. $$\int _{}^{}\frac{sec ^{2} x}{{\rm \cosec}^{2} x} , dx=\tan x-x+C$$

11. $$\int \sqrt{1+\sin 2x} , dx=-\cos x+\sin x+C$$

### This Post Has 4 Comments

1. Sir will you upload videos that year for class 12th

1. The information regarding this will be posted on the website after the 21 days lock-down.

2. How to get assignments? I am registered.

1. As mentioned in the perks of membership, you can access the notes and assignments typed on the website, along with their video explanations.