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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Integral using substitution/parts

**Physics Forums | Science Articles, Homework Help, Discussion**