# Questions tagged [integration]

Concerns all aspects of integration, including the integral definition and computational methods. For questions solely about the properties of integrals, use in conjunction with (indefinite-integral), (definite-integral), (improper-integrals) or another tag(s) that typically describe(s) the types of the integrals being considered. This tag often goes along with the (calculus) tag.

56,519 questions
Filter by
Sorted by
Tagged with
16 views

### numerical integration of a Differential Equation in C++ [closed]

I need to find a definite integral of an equation in C++. dy/dt=(v/L)sin(y +(v/L)*ln[cos(Kt+a)] - b) v, L, K, a, b are constants, 'y' is a function of 't'. Now, I need to find the integral of 'y' ...
25 views

### How to show that $J_{n+1} = \frac{3n-1}{3n} J_n$?

Let $$J_n := \int_{0}^{\infty} \frac{1}{(x^3 + 1)^n} \, {\rm d} x$$ where $n > 2$ is integer. How to show that $J_{n+1} = \frac{3n-1}{3n} J_n$?
12 views

### Change of variables in integrals

Im trying to understand what kind of variable change in integrals is legit. In my book's it states that the function the deriviative of the function that we change should be continious, but I've seen ...
59 views

### Find $\int\,\frac 4 { x \sqrt{x+1} }\,\text{d}x$

Calculate $$\int \,\frac 4 { x \sqrt{x+1} } \,\text{d}x\,.$$ My attempt: I tried substituting $u=\sqrt{x+1}$, so $u^2=x+1$, but it didn't get me anywhere.
12 views

35 views

123 views

### Evaluate $\int_0^{\infty} x^2\ln(\sinh x)\operatorname{sech}(3 x){\rm d}x$.

Problem Evaluate $\displaystyle\int_0^{\infty} x^2\ln(\sinh x)\operatorname{sech}(3 x){\rm d}x .$ Someone writes as follows \begin{align*} &\int_0^{\infty} x^2\ln(\sinh x)\operatorname{sech}(3 ...
23 views

### Calculation partial derivatives

Lets assume $Y = X^2$ $Z = \frac{1}{n} \sum_1^n Y_i$ $\frac{\partial Z}{\partial X} = \frac{X}{2}$ How partial derivative of $Z$ with respect to $X$ is Calculated? More Detailed info here
34 views

### Is this a sufficient condition for the integral to be greater than $m$?

It is given that $f:\mathbb R \to \mathbb R$ is positive continuous function. If it is positive then it means that it never goes below the $x-$ axis. I want to find a sufficient condition such that we ...
16 views

54 views

### Evaluating $\int _0^{\infty }e^{x\left(t-p\right)}p^{1-e^{-px}}\:dx$

How do I proceed with this integration? When I try integration by parts, the same thing keeps coming over and over again. $$I=\int_0^\infty e^{x(t-p)}p^{1-e^{-px}}\,dx$$