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# 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
2 years, 1 month 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. · 2 years ago

All CBSE NCERT Class 12 questions · 2 years ago

Yep. Thanks! · 2 years 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 · 2 years, 1 month ago

They are quite unreadable @Kartik Sharma · 2 years, 1 month ago

Can anyone do this https://brilliant.org/discussions/thread/extremely-weird-integration/?ref_id=946409 · 1 year, 4 months ago