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અનિયત સંકલન

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ગણિત ધોરણ 12 સિમેસ્ટર 4

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ગણિત

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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

Answer

    • 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

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

    integral space straight x squared space times space straight e to the power of 3 straight x end exponent space dx space equals space straight x squared space integral space straight e to the power of 3 straight x end exponent space dx space minus space integral space open square brackets straight d over dx space open parentheses straight x squared close parentheses space integral space straight e to the power of 3 straight x end exponent space dx close square brackets space dx

                      
                           equals space straight x squared space times space fraction numerator straight e cubed space straight x over denominator 3 end fraction space minus space integral space 2 straight x space times space fraction numerator straight e cubed space straight x over denominator 3 end fraction space dx equals space fraction numerator straight x squared space straight e to the power of 3 straight x end exponent over denominator 3 end fraction space minus space 2 over 3 space integral space straight x space times space straight e to the power of 3 straight x end exponent space dx equals space fraction numerator straight x squared space straight e to the power of 3 straight x end exponent over denominator 3 end fraction space minus space 2 over 3 space open square brackets straight x space integral space straight e to the power of 3 straight x end exponent space dx space minus integral space open square brackets straight d over dx space open parentheses straight x close parentheses space integral space straight e to the power of 3 straight x end exponent space dx close square brackets space dx close square brackets equals space fraction numerator straight x squared space straight e to the power of 3 straight x end exponent over denominator 3 end fraction space minus space 2 over 3 space open square brackets xe to the power of 3 straight x end exponent over 3 space minus space integral space 1 space times space straight e to the power of 3 straight x end exponent over 3 space dx close square brackets equals space fraction numerator straight x squared space straight e to the power of 3 straight x end exponent over denominator 3 end fraction space minus space 2 over 3 space open square brackets xe to the power of 3 straight x end exponent over 3 space minus space 1 third space integral space straight e to the power of 3 straight x end exponent space dx close square brackets equals space fraction numerator straight x squared space straight e to the power of 3 straight x end exponent over denominator 3 end fraction space minus space 2 over 3 space open square brackets xe to the power of 3 straight x end exponent over 3 space minus space 1 third space times straight e to the power of 3 straight x end exponent over 3 space dx space close square brackets space plus space straight c



                           equals space fraction numerator straight x squared space straight e to the power of 3 straight x end exponent over denominator 3 end fraction space minus space fraction numerator 2 space xe to the power of 3 straight x end exponent over denominator 9 end fraction space plus space fraction numerator 2 space straight e to the power of 3 straight x end exponent over denominator 27 end fraction space plus space straight c bold equals bold space bold e to the power of bold 3 bold x end exponent bold space open parentheses bold x to the power of bold 2 over bold 3 bold space bold minus bold space bold 2 over bold 9 bold space bold x bold space bold plus bold space bold 2 over bold 27 close parentheses bold space bold plus bold space bold c
    Answer
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    નીચેનાં વિધેયનું x વિશે સંકલિત મેળવો :
    (3 + 5x) cos 7x

    Answer

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

    Answer
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