We've been focusing on integration by parts or by substitution and i can't figure some out:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \int 4x^3\tan^-1xdx [/tex] Here [tex]\tan^-1x[/tex] means inverse tanx. I cant get the latex right for it.

my working so far:

[tex] By parts,

u = \tan^-1x , \frac{dv}{dx} = 4x^3,

\frac{du}{dx} = \frac{1}{1 + x^2}, v = \frac{4x^4}{4} = x^4

\Rightarrow x^4\tan^-1 - \int\frac{x^4}{1 + x^2} [/tex]

It's the Integral [tex]\int\frac{x^4}{1 + x^2}[/tex] that i can't do ???

The one i'm completely stuck on how to even start is:

Find the general solution x(t) of the differential equation

[tex] \frac{dx}{dt} = \frac{t^2 + 3t + 5}{t^2 + 6t +34} [/tex]

and the particular solution for which x(-3) = 0.

Can anyone help?

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# Homework Help: Integral using substitution/parts

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