# Lecture 5 Type 2 Integrals Class 12 Maths

## Part - 2 Lecture - 5 Chapter 7 Integrals

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HOTS Questions discussed in this video:

3. $\int\frac{(x^4-x)^\frac{1}{4}}{x^5}dx=\frac{4}{15}\left(1-\frac{1}{x^3}\right)^\frac{5}{4}+C$

4. $\int{\frac{1}{x\sqrt{ax-x^2}}dx=-\frac{2}{a}\sqrt{\frac{(a-x)}{x}}}+C$

5. $\int_{\frac{1}{3}}^{1}\frac{(x-x^3)^\frac{1}{3}}{x^4}dx=6$

6. $\int \frac{1}{x^2(x^4+1)^\frac{3}{4}}dx=-\left(1+\frac{1}{x^4}\right)^\frac{1}{4}+C$

7. $\int\frac{\sqrt{x^2+1}(\log{(}x^2+1)-2\log{x})}{x^4}dx=-\frac{1}{3}\left(1+\frac{1}{x^2}\right)^\frac{3}{2}\left[\log{\left(1+\frac{1}{x^2}\right)}-\frac{2}{3}\right]+C$