Evaluate the following integral: from Mathematics Integrals
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    Integrals

    Multiple Choice QuestionsShort Answer Type

    51.

    Explain the following integral:
    space integral subscript 0 superscript 1 fraction numerator 1 over denominator 1 plus straight x squared end fraction dx

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    Answer
    52.

    Explain the following integral:
    integral subscript 2 superscript 3 fraction numerator 1 over denominator straight x squared minus 1 end fraction dx

    89 Views
    Answer
    53.

    Explain the following integral:
    integral subscript 2 superscript 3 fraction numerator straight x over denominator straight x squared plus 1 end fraction dx

    88 Views
    Answer
    54. Evaluate the following integral:
    integral subscript 1 superscript 2 fraction numerator dx over denominator left parenthesis straight x plus 1 right parenthesis space left parenthesis straight x plus 2 right parenthesis end fraction
    92 Views
    Answer
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    55. Evaluate the following integral:
    integral subscript 1 superscript 2 fraction numerator 5 straight x squared over denominator straight x squared plus 4 straight x plus 3 end fraction dx

    Let I = integral subscript 1 superscript 2 fraction numerator 5 straight x squared over denominator straight x squared plus 4 straight x plus 3 end fraction dx space equals space 5 integral subscript 1 superscript 2 fraction numerator straight x squared over denominator left parenthesis straight x plus 1 right parenthesis space left parenthesis straight x plus 3 right parenthesis end fraction dx

           equals space 5 integral subscript 1 superscript 2 open square brackets 1 plus fraction numerator left parenthesis negative 1 right parenthesis squared over denominator left parenthesis straight x plus 1 right parenthesis space left parenthesis negative 1 plus 3 right parenthesis end fraction plus fraction numerator left parenthesis negative 3 right parenthesis squared over denominator left parenthesis negative 3 plus 1 right parenthesis space left parenthesis straight x plus 3 right parenthesis end fraction close square brackets dx equals space 5 integral subscript 1 superscript 2 open square brackets 1 plus fraction numerator 1 over denominator 2 left parenthesis straight x plus 1 right parenthesis end fraction minus fraction numerator 9 over denominator 2 left parenthesis straight x plus 3 right parenthesis end fraction close square brackets dx equals space 5 open square brackets straight x plus 1 half log left parenthesis straight x plus 1 right parenthesis minus 9 over 2 log left parenthesis straight x plus 3 right parenthesis close square brackets subscript 1 superscript 2

          equals space 5 space open square brackets straight x plus 1 half log left parenthesis straight x plus 1 right parenthesis minus 9 over 2 log left parenthesis straight x plus 3 right parenthesis close square brackets subscript 1 superscript 2 equals space 5 open square brackets open parentheses 2 plus 1 half log 3 minus 9 over 2 log 5 close parentheses space minus space open parentheses 1 plus 1 half log 2 minus 9 over 2 log 4 close parentheses close square brackets equals space 5 open square brackets 1 plus 1 half log 3 minus 9 over 2 log 5 minus 1 half log 2 plus 9 over 2 log 4 close square brackets equals space 5 open square brackets 1 plus 1 half left parenthesis log 3 minus log 2 right parenthesis minus 9 over 2 left parenthesis log space 5 space minus log space 4 right parenthesis close square brackets equals space 5 open square brackets 1 plus 1 half log open parentheses 3 over 2 close parentheses minus 9 over 2 log open parentheses 5 over 4 close parentheses close square brackets

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    56. Evaluate the following integral
    space integral subscript 2 superscript 3 fraction numerator 1 over denominator straight x squared minus 1 end fraction dx
    93 Views
    Answer
    57. Evaluate the following integral:
    space space integral subscript 0 superscript 4 fraction numerator dx over denominator square root of straight x squared plus 2 straight x plus 3 end root end fraction
    96 Views
    Answer
    58. Evaluate the following integral:
    integral subscript 4 superscript 9 fraction numerator square root of straight x over denominator open parentheses 30 minus straight x to the power of begin display style 3 over 2 end style end exponent close parentheses squared end fraction dx
    137 Views
    Answer
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    59.

    Evaluate the following definite integral
    integral subscript 0 superscript 2 fraction numerator 6 straight x plus 3 over denominator straight x squared plus 4 end fraction dx.

    94 Views
    Answer
    60.

    Evaluate the following definite integral
    integral subscript 0 superscript 1 fraction numerator 2 straight x over denominator 5 straight x squared plus 1 end fraction dx

    92 Views
    Answer
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