# Integration Practice!

Image Credit: Patrick JMT

I am just sharing it because I think they are good. I hope they are quite readable.

Note by Kartik Sharma
3 years, 6 months ago

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1. $$\displaystyle\int \dfrac{\sin x + \sec x}{\tan x}\text{ d}x$$

2. $$\displaystyle\int \dfrac{x}{\sqrt{3+x^4}}\text{ d}x$$

3. $$\displaystyle\int \dfrac{x}{x^4+x^2+1}\text{ d}x$$

4. $$\displaystyle\int \sin^3\theta\cos^5\theta\text{ d}\theta$$

5. $$\displaystyle\int \dfrac{\sqrt{1+\ln x}}{x\ln x}\text{ d}x$$

6. $$\displaystyle\int \dfrac{e^{2t}}{1+e^{4t}}\text{ d}t$$

7. $$\displaystyle\int e^{\sqrt[3]{x}}\text{ d}x$$

8. $$\displaystyle\int (1+\sqrt{x})^6\text{ d}x$$

9. $$\displaystyle\int \ln (x^2-1)\text{ d}x$$

10. $$\displaystyle\int_{-2}^{2} |x^2-4x| \text{ d}x$$

11. $$\displaystyle\int \sqrt{1+e^x}\text{ d}x$$

12. $$\displaystyle\int \dfrac{x+a}{x^2+a^2}\text{ d}x$$

13. $$\displaystyle\int (x+\sin x)^2\text{ d}x$$

14. $$\displaystyle\int \dfrac{1}{e^{3x}-e^x}\text{ d}x$$

15. $$\displaystyle\int \sqrt{x}e^{\sqrt{x}}\text{ d}x$$

16. $$\displaystyle\int \dfrac{x^3}{(x+1)^{10}}\text{ d}x$$

17. $$\displaystyle\int \dfrac{\tan^{-1}\sqrt{x}}{\sqrt{x}}\text{ d}x$$

18. $$\displaystyle\int \dfrac{\text{ d}x}{e^x-e^{-x}}$$

19. $$\displaystyle\int \sin x \cdot \sin 2x\cdot \sin 3x\text{ d}x$$

20. $$\displaystyle\int \dfrac{1}{\sqrt{x+1}+\sqrt{x}}\text{ d}x$$

Sorry for any errors.

- 3 years, 5 months ago

All CBSE NCERT Class 12 questions

- 3 years, 5 months ago

Yep. Thanks!

- 3 years, 5 months ago

It is slightly hard to read it, because the image is rather small and zooming in loses the focus. Can you type out some of these? The integrals look interesting to work on!

Staff - 3 years, 5 months ago

They are quite unreadable @Kartik Sharma

- 3 years, 5 months ago

- 2 years, 9 months ago

They are easy

- 3 years, 5 months ago