How to find the indefinite integral of (x + 1) / (x ^ 2 + 2x)?
A:
∫[(x+1)/(x^2+2x)]dx
=(1/2) ∫ {1/[(x+1)^2-1]} d [(x+1)^2-1]
=(1/2) ln[(x+1)^2-1]+C
=(1/2)ln|x^2+2x|+C
RELATED INFORMATIONS
- 1. It is proved that 3arccosx arccos (3x-4x & # 178;) = π, (- 1 / 2 ≤ x ≤ 1 / 2)
- 2. Y = 1 + sin (2x) + 2cos ^ 2 (x) = 1 + sin (2x) + 1 + cos (2x) = 2 + sin (2x) + cos (2x) = 2 + √ 2Sin (2x + π / 4), so the period is π =2 + √ 2Sin (2x + π / 4)
- 3. Expressing arcsin5 / 13 + arccos (- 3 / 5) with an inverse trigonometric function value I want to ask why the final inverse triangle is expressed in COS instead of sin Is there anything particular about using sin or cos
- 4. If x is the smallest internal angle in a triangle, then the range of the function y = SiNx + cosx is () A. [12,22]B. (0,32]C. (1,2]D. (12,22]
- 5. If x is an internal angle of a triangle, then what is the range of the function y = SiNx + cosx? Why 45
- 6. How to calculate the integral of 1 / ((SiNx + cosx) ^ 2)? RT
- 7. Y = (SiNx + cosx) ^ 2 + 2cosx ^ 2, find the decreasing interval, maximum and minimum
- 8. Find the minimum positive period of F (x) = SiNx / 2 quartic power + cosx / 2 quartic power + quarter root sign three times sin2x
- 9. If the maximum value of the function y = a SiNx + 3cosx + 1 is 6, then a=
- 10. If the curve V is the square of the surface y = x, y = x, x + y + Z = 2, and z = 0 is the defined area, then fffdxdydz =? Calculus
- 11. Finding indefinite integral ∫ (e ^ 2x) / (2 + e ^ x) DX Such as the title
- 12. (x ^ 2 + 1) / ((x + 2) ^ 2 (x ^ 2 + 2x + 3) ^ 2) indefinite integral
- 13. ∫ (3-2x) ^ 3DX for indefinite integral
- 14. Indefinite integral (x + 2) / (x ^ 2 + 2x + 2)
- 15. D (∫ Sint / TDT) / DX (upper limit 2x, lower limit 2)
- 16. Find the limit cost ^ 2DT / X when x approaches to 0, where cost ^ 2DT is the definite integral of line X and line 0
- 17. Seeking indefinite integral ∫ (xsinx) 178; DX
- 18. Calculating indefinite integral ∫ (2-xsinx) / X DX Calculating indefinite integral ∫ (2-xsinx) / X DX
- 19. How to calculate indefinite integral (x ^ 4-2) / (x ^ 2 + 1) DX?
- 20. How to calculate the indefinite integral of x ^ 4 / x ^ 2-1?