# integration's questions - English 1answer

42.718 integration questions.

### 2 Closed-form solution for an integral with integer power rational function

1 answers, 24 views calculus integration
I need a closed-form solution for the following integral: $$\int_{0}^{\infty}\frac{dt}{(t+a)^{m} (t +b)^{n}};\,\,a,b>0;\,\,m,n\geq1\,\text{are integers}$$ If $m$ and $n$ are non-integers, I can ...

### 1 Why do we ignore constant produced by integration of derivative when we derive integration by parts formula?

2 answers, 24 views calculus integration
My question is somehow related to this question. What I would like to know is why we ignore the fact that integral of derivative of f(x) is equal to ...

### substitution for a multiple integral

1 answers, 23 views integration substitution jacobian
I came across a concept which I have never dealt with before. I had an idea but it is flawed and I would like to know why it is flawed. To those who are familiar with that subject it will seem ...

### 1 generalized Riemann Integrability of $f\cdot g$

Let $\mathcal{R}([a.b])$ the set of all Riemann-integrable functions in $[a,b]$. Let $\mathcal{R}^{*}([a,b])$ the set of all Generalized Riemann-Integrable functions in $[a,b]$ (I'm talking about the ...

### 1 $\lim_{\epsilon\rightarrow 0^{+}}{\int_{0}^{\infty}\,e^{-\epsilon x}\,\frac{|\sin{x}|^{t}} {x^{t-1}}\,dx}, \quad 1< t<2$

let $1<t<2$. I need to evaluate $$\lim_{\epsilon\rightarrow 0^{+}}\int_{0}^{\infty}\,e^{-\epsilon x}\,\frac{|\sin{x}|^{t}} {x^{t-1}}\,dx$$ If $t>2$ one can easily apply the dominated ...

### 38 Is there a chain rule for integration?

6 answers, 79.783 views calculus integration
I know the chain rule for derivatives. The way as I apply it, is to get rid of specific 'bits' of a complex equation in stages, i.e I will derive the $5$th root first in the equation $(2x+3)^5$ and ...

### 20 Class of integrals: $I(a)=\int_0^\infty \frac{dx}{e^x+ax}$

I'm investigating integrals in the form $$I(a):=\int_0^\infty \frac{dx}{e^x+ax}$$ So far, I haven't been able to find any special values other than $I(0)=1$, and I've only managed to evaluate these ...

### Definition of a positively integrable function

1 answers, 19 views integration lebesgue-integral