Notes: What is integral of function 3x^2/x^3+1 ?

Monday, March 17, 2014

What is integral of function 3x^2/x^3+1 ?

To solve the indefinite integral of the given function,
we'll have to use substitution method because we notice that the numerator of the
fraction represents the derivative of the denominator of this
fraction.

Let $\displaystyle{{x}}^{{3}}+{1}={t}$
.

We'll differentiate both
sides:

$\displaystyle{3}{{x}}^{{2}}{\left.{d}{x}\right.}={\left.{d}{t}\right.}$

We'll
compute the integral:

$\displaystyle\int\frac{{{3}{{x}}^{{2}}{\left.{d}{x}\right.}}}{{{{x}}^{{3}}+{1}}}=\int$
dt/t

$\displaystyle\int\frac{{\left.{d}{t}}}{{t}}={\ln}{\left|{t}\right|}+$
C

We'll replace t by $\displaystyle{{x}}^{{3}}+{1}$ and we'll
get:

$\displaystyle\int\frac{{{3}{{x}}^{{2}}{\left.{d}{x}\right.}}}{{{{x}}^{{3}}+{1}}}={\ln}{\left|{{x}}^{{3}}+{1}\right|}+$
C

Therefore, the requested indefinite
integral of the given function is $\displaystyle\int\frac{{{3}{{x}}^{{2}}{\left.{d}{x}\right.}}}{{{{x}}^{{3}}+{1}}}={\ln}{\left|{{x}}^{{3}}+{1}\right|}+{C}$

Notes

Monday, March 17, 2014

What is integral of function 3x^2/x^3+1 ?

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What is the meaning of the 4th stanza of Eliot's Preludes, especially the lines "I am moved by fancies...Infinitely suffering thing".

Monday, March 17, 2014

What is integral of function 3x^2/x^3+1 ?

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Post a Comment

What is the meaning of the 4th stanza of Eliot&#39;s Preludes, especially the lines &quot;I am moved by fancies...Infinitely suffering thing&quot;.

What is the meaning of the 4th stanza of Eliot's Preludes, especially the lines "I am moved by fancies...Infinitely suffering thing".