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Table of Integrals

1. \(\int dx=x+C\)

2. \(\int x^{\alpha}dx=\frac{x^{\alpha+1}}{\alpha+1}+C\)

3. \(\int \frac{dx}{x}=\ln |x|+C\)

4. \(\int a^x dx=\frac{a^x}{\ln a}+C\)

5. \(\int e^x dx=e^x+C\)

6. \(\int \sin x dx=-\cos x+C\)

7. \(\int \cos x dx=\sin x+C\)

8. \(\int \frac{dx}{\cos^2 x}=tg x+C\)

9. \(\int \frac{dx}{sin^2 x}=-ctg x+C\)

10. \(\int \frac{dx}{\sqrt{a^2-x^2}}=\arcsin\frac{x}{a}+C\)

11. \(\int \frac{dx}{\sqrt{x^2 \pm a^2}}=\ln\left|x+\sqrt{x^2\pm a^2}\right|+C\)

12. \(\int \frac{dx}{x^2+a^2}=\frac{1}{a}arctg\frac{x}{a}+C\)

13. \(\int \frac{dx}{x^2 -a^2}=\frac{1}{2a}\ln\left|\frac{x-a}{x+a}\right|+C\)

14. \(\int sh x dx = ch x+C\)

15. \(\int ch x dx = sh x+C\)

16. \(\int \frac{dx}{ch^2 x} = th x+C\)

17. \(\int \frac{dx}{sh^2 x} = -cth x+C\)

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