1
vote
0answers
20 views

Laplace transform of Differential Equation with a piecewise function

Hi I have this question and I am horribly stuck at one part and I cant seem to figure out if i did something wrong so any advice or help would be greatly apprecaited. Here is the question: ...
2
votes
1answer
108 views

Partial fraction decomposition of $\frac{1}{x^{2n}+a^{2n}}$

I came across a formula for the partial fraction decomposition of $ \displaystyle \frac{1}{x^{2n}+a^{2n}}$. It seems correct (at least for $n=1,2$, and $3$). But how is it derived? ...
5
votes
1answer
198 views

Find the following integral: [duplicate]

Find $$\int \sqrt{\tan x}dx$$ My attempt: $$\text{Let}\ I=\int \sqrt{\tan(x)}dx$$ $$\text{Let}\ u=\tan(x), du=(1+\tan^{2}(x))dx$$ $$I=\int \frac{\sqrt{u}}{u^{2}+1}$$ $$\text{Let}\ v=\sqrt{u}, ...
4
votes
3answers
654 views

Partial Fractions Expansion of $\tanh(z)/z$

I have seen the following formula in papers (without citations) and in Mathematica's documentation about Tanh[]: $$ \frac{\tanh(z)}{8z}=\sum_{k=1}^{\infty} ...