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અનિયત સંકલન

નીચેનાં વિધેયનું x વિશે સંકલિત મેળવો :
$straight x squared space log space straight x space semicolon space straight x space greater than space 0$

નીચેનાં વિધેયનું x વિશે સંકલિત મેળવો :
$cos to the power of negative 1 end exponent space straight x space semicolon space straight x space element of space open square brackets negative 1 comma space 1 close square brackets$

નીચેનાં વિધેયનું x વિશે સંકલિત મેળવો :
$straight x squared space straight e to the power of 3 straight x end exponent$

નીચેનાં વિધેયનું x વિશે સંકલિત મેળવો :
(3 + 5x) cos 7x

નીચેનાં વિધેયનું x વિશે સંકલિત મેળવો :
$straight x squared space tan to the power of negative 1 end exponent space straight x$

straight I space equals space integral space straight x squared space tan to the power of negative 1 end exponent space straight x space dx

equals space tan to the power of negative 1 end exponent space straight x space times space straight x cubed over 3 space minus space integral space fraction numerator 1 over denominator 1 space plus space straight x squared end fraction space straight x cubed over 3 space dx equals space straight x cubed over 3 space tan to the power of negative 1 end exponent space straight x space minus space 1 third space integral space fraction numerator straight x cubed over denominator 1 space plus space straight x squared end fraction space dx equals space straight x cubed over 3 space tan to the power of negative 1 end exponent space straight x space minus space 1 third space straight I subscript 1

જ્યાં, $straight I subscript 1 space equals space integral space fraction numerator straight x cubed over denominator 1 space plus space straight x squared end fraction space dx space semicolon space 1 space plus space straight x squared space equals space straight t$ લેતાં, $xdx space equals space 1 half space dt$

વળી,

$straight I subscript 1 space equals space integral space fraction numerator straight x squared space times space straight x space dx over denominator 1 space plus space straight x squared end fraction therefore space straight I subscript 1 space equals space integral space fraction numerator open parentheses straight t space minus space 1 close parentheses space begin display style 1 half end style space dt over denominator straight t end fraction$

$equals space 1 half space integral space open parentheses 1 space minus space 1 over straight t close parentheses space dt equals space 1 half space open square brackets straight t space minus space log space open vertical bar space straight t space close vertical bar close square brackets space plus space straight c subscript 1 equals space 1 half space open square brackets 1 space plus space straight x squared space minus space log space open parentheses 1 space plus space straight x squared close parentheses close square brackets space plus space straight c subscript 1$

$therefore space straight I space equals space straight x cubed over 3 space tan to the power of negative 1 end exponent space straight x space minus space 1 over 6 space open square brackets straight x squared space minus space log space open parentheses 1 space plus space straight x squared close parentheses close square brackets space plus space straight c space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space જ ્ ય ાં comma space straight c space equals space minus 1 third space straight c subscript 1 space minus space 1 over 6 therefore space integral space straight x squared space tan to the power of negative 1 end exponent space straight x space dx bold space bold space bold space bold equals bold space bold x to the power of bold 3 over bold 3 bold space bold tan to the power of bold minus bold 1 end exponent bold space bold x bold space bold minus bold space bold 1 over bold 6 bold space open square brackets bold x to the power of bold 2 bold space bold minus bold space bold log bold space open parentheses bold 1 bold space bold plus bold space bold x to the power of bold 2 close parentheses close square brackets bold space bold plus bold space bold c$

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