Integral tabele 1

Te zgjidhen integralet

 

a-)  \int x^3 \mathrm{d}x=          b-) \int x^{-4} \mathrm{d}x=   

c-) \int x^{\frac{3}{5}} \mathrm{d}x=          d-) \int x^{\pi} \mathrm{d}x= 

 

Zgjidhje

Udhezim: Shikojme tek tabela e integraleve se me ke integral ngjasojne.

\int x^n \mathrm{d}x=\frac{x^{n+1}}{n+1} + c, \quad n\neq-1   

 

a-)

\int x^3 \mathrm{d}x=\frac{x^{3+1}}{3+1} + c=\frac{x^{4}}{4} + c 

 

b-)

\int x^{-4} \mathrm{d}x=\frac{x^{-4+1}}{-4+1} + c=\frac{x^{-3}}{-3} + c= 

=\frac{\frac{1}{x^3}}{-3}  + c=\frac{x^{-3}}{-3} + c=\frac{1}{3x^{3}} + c 

 

c-)

\int x^{\frac{3}{5}} \mathrm{d}x= \frac{x^{\frac{3}{5}+1}}{\frac{3}{5}+1} + c= 

= \frac{x^{\frac{8}{5}}}{\frac{8}{5}} + c=\frac{5x^{\frac{8}{5}}}{8} + c 

 

d-)

\int x^{\pi} \mathrm{d}x=\frac{x^{{\pi}+1}}{{\pi}+1} + c 

 

 

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