Integral Tabele 1 | Matematika

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-)

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