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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: indefinite integration 3
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[Post New]28 Aug 2008 23:59:53 IST
    Subject: indefinite integration 3
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reddevil_2009 (1410)

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[Post New]29 Aug 2008 01:21:33 IST
    Subject: Re:indefinite integration 3
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sachinguptaiit (964)

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\large{\text{$\int a^{px}\;b^{qx}dx$}}


\large{\text{$\int \left(a^pb^q\right)^xdx$}}


\large{\text{$\frac{\left({a^pb^q\right)^x}}{\left(\ln(a^pb^q)\right)}$}}
"Before you start some work, always ask yourself three questions - Why am I doing it, What the results might be and Will I be successful. Only when you think deeply and find satisfactory answers to these questions, go ahead."

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[Post New]29 Aug 2008 01:54:42 IST
    Subject: Re:indefinite integration 3
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\large{\text{$\int x^3(\ln(x))^2$}}


\large{\text{\emph{Put $x$ = $e^t$}}}


\large{\text{$\int t^2e^{4t}dt$}}


\large{\text{$\frac{t^2e^{4t}}{4}-\frac{1}{2}\int te^{4t}dt$}}


\large{\text{$\frac{t^2e^{4t}}{4}-\frac{te^{4t}}{8}+\frac{e^{4t}}{32}+c$}}


\large{\text{$\frac{(\ln(x))^2e^{4\ln(x)}}{4}-\frac{\ln(x)e^{4\ln(x)}}{8}+\frac{e^{4\ln(x)}}{32}+c$}}


\large{\text{$\frac{(\ln(x))^2x^4}{4}-\frac{\ln(x)x^4}{8}+\frac{x^{4}}{32}+c$}}


 
"Before you start some work, always ask yourself three questions - Why am I doing it, What the results might be and Will I be successful. Only when you think deeply and find satisfactory answers to these questions, go ahead."

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[Post New]29 Aug 2008 02:06:54 IST
    Subject: Re:indefinite integration 3
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\large{\text{$-\frac{1}{2}\int-2\sqrt{1+\frac{1}{x^2}}\frac{\ln\left(1+\frac{1}{x^2}\right)}{x^3}dx$}}


\large{\text{\emph{Put }$1+\frac{1}{x^2}=t^2$}}


\large{\text{$-\int t\ln\left(t\right)dt$}}


\large{\text{$-\left(\ln(t).\frac{t^2}{2}-\frac{t^2}{4}\right)+c$}}


\large{\text{$\left(\frac{t^2}{4}-\ln(t).\frac{t^2}{2}\right)+c$}}


\large{\text{$\left(\frac{\left(\sqrt{1+\frac{1}{x^2}}\right)^2}{4}-\ln\left(\sqrt{1+\frac{1}{x^2}}\right).\frac{\left(\sqrt{1+\frac{1}{x^2}}\right)^2}{2}\right)+c$}}
"Before you start some work, always ask yourself three questions - Why am I doing it, What the results might be and Will I be successful. Only when you think deeply and find satisfactory answers to these questions, go ahead."

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[Post New]30 Aug 2008 21:39:11 IST
    Subject: Re:indefinite integration 3
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nitish971 (407)

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1) I =


Put


Thus


I =


 =   + c


 Resubstituting t,
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[Post New]31 Aug 2008 14:17:07 IST
    Subject: Re:indefinite integration 3
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karthik.n.n (5)

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whenever u see indefinite integral like that a to the power stuff see whether u see any derivati of the substitution and get rid of the problem
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