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İntegral sorusunu çözebilecek var mııı

İntegral Sorusunu Çözebilecek Var Mııı class=

Sagot :

Jakindarans

Cevap:

Adım adım açıklama:

[tex]\int {\frac{x^2-1+1}{x+1} } \, dx \\\\\int {\frac{(x-1)(x+1)+1}{x+1} } \, dx\\\\\int {(x-1)} \, dx+ \int {\frac{1}{x+1} } \, dx \\\\\frac{x^{2} }{2} -x+ln|x+1| +c[/tex]

Enesaksan17rans

Cevap:

[tex]\frac{x^2}{2} -x+ln|x+1|+C[/tex]

Adım adım açıklama:

[tex]\frac{x^2}{x+1} =x-\frac{x}{x+1} =x-(1-\frac{1}{x+1} )=x-1+\frac{1}{x+1}[/tex]

[tex]\int {\frac{x^2}{x+1} } \, dx =\int {(x-1+\frac{1}{x+1}) \, dx =\int {x \, dx-\int {1 \, dx+\int {\frac{1}{x+1} \, dx[/tex]

[tex]\int {x \, dx-\int {1 \, dx+\int {\frac{1}{x+1} \, dx=\frac{x^2}{2} -x+ln|x+1|+C[/tex]

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