Question

purre 100 points

⏩List some formulae of integration
⏩Aslo find the integration of :

$\sqrt{ \sin(x) }$
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Answer 1

∫1dx=x+c

2)∫adx=ax+c

where a is any constant.

3)∫xndx=xn+1n+1+c

∫xndx=xn+1n+1+c

4)∫[f(x)]nf′(x)dx=[f(x)]n+1n+1+c

∫[f(x)]nf′(x)dx=[f(x)]n+1n+1+c

5)∫1xdx=lnx+c

∫1xdx=ln⁡x+c

6)∫f′(x)f(x)dx=lnf(x)+c

∫f′(x)f(x)dx=ln⁡f(x)+c

7)∫axdx=axlna+c

∫axdx=axln⁡a+c

8)∫af(x)dx=af(x)lna+c

∫af(x)dx=af(x)ln⁡a+c

9)∫exdx=ex+c

∫exdx=ex+c

10)∫ef(x)dx=ef(x)+c

∫ef(x)dx=ef(x)+c

11)∫af(x)dx=a∫f(x)

∫af(x)dx=a∫f(x)

12)∫[f(x)±g(x)]dx=∫f(x)dx±∫g(x)dx

∫[f(x)±g(x)]dx=∫f(x)dx±∫g(x)dx

13)∫f(x)⋅g(x)dx=f(x)(∫g(x)dx)−∫[f′(x)(∫g(x)dx)]dx

∫f(x)⋅g(x)dx=f(x)(∫g(x)dx)−∫[f′(x)(∫g(x)dx)]dx

14)∫lnxdx=x(lnx−1)+c

∫ln⁡xdx=x(ln⁡x−1)+c

15)∫sinxdx=−cosx+c

∫sin⁡xdx=−cos⁡x+c

16)∫cosxdx=sinx+c.

here is ur required answer.

plz mark it as brainliest.

Answer 2

Integration of sin x = cos x