Intergral cheet sheet

Common Integrals Quizlet

Question & Answer Format:

1. Q: What is the integral of dxdx?
   A: x+Cx + C

2. Q: What is the integral of xndxx^n dx, where n≠−1n \neq -1?
   A: xn+1n+1+C\frac{x^{n+1}}{n+1} + C

3. Q: What is the integral of exdxe^x dx?
   A: ex+Ce^x + C

4. Q: What is the integral of axdxa^x dx?
   A: axln⁡a+C\frac{a^x}{\ln a} + C

5. Q: What is the integral of x−1dxx^{-1} dx?
   A: ln⁡∣x∣+C\ln|x| + C

6. Q: What is the integral of eaxdxe^{ax} dx?
   A: 1aeax+C\frac{1}{a} e^{ax} + C

7. Q: What is the integral of cos⁡xdx\cos x dx?
   A: sin⁡x+C\sin x + C

8. Q: What is the integral of sin⁡xdx\sin x dx?
   A: −cos⁡x+C-\cos x + C

9. Q: What is the integral of sec⁡xtan⁡xdx\sec x \tan x dx?
   A: sec⁡x+C\sec x + C

10. Q: What is the integral of csc⁡xcot⁡xdx\csc x \cot x dx?
    A: −csc⁡x+C-\csc x + C

11. Q: What is the integral of sec⁡2xdx\sec^2 x dx?
    A: tan⁡x+C\tan x + C

12. Q: What is the integral of csc⁡2xdx\csc^2 x dx?
    A: −cot⁡x+C-\cot x + C

13. Q: What is the integral of dxx2+a2\frac{dx}{x^2 + a^2}?
    A: 1atan⁡−1(xa)+C\frac{1}{a} \tan^{-1} \left( \frac{x}{a} \right) + C

14. Q: What is the integral of xdxx2+a2\frac{x dx}{x^2 + a^2}?
    A: 12ln⁡∣x2+a2∣+C\frac{1}{2} \ln|x^2 + a^2| + C

15. Q: What is the integral of tan⁡xdx\tan x dx?
    A: ln⁡∣sec⁡x∣+C\ln|\sec x| + C

16. Q: What is the integral of cot⁡xdx\cot x dx?
    A: ln⁡∣sin⁡x∣+C\ln|\sin x| + C

17. Q: What is the integral of sec⁡xdx\sec x dx?
    A: ln⁡∣sec⁡x+tan⁡x∣+C\ln|\sec x + \tan x| + C

18. Q: What is the integral of csc⁡xdx\csc x dx?
    A: ln⁡∣csc⁡x−cot⁡x∣+C\ln|\csc x - \cot x| + C

Note: CC represents the constant of integration.