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Conreu
  • Member for 2 years, 4 months
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  • Catalunya
6 votes
Accepted

Calculate integral $\int\limits_{0}^{\infty }xe^{-nx}\cos xdx$

5 votes

$\lim\limits_{x\to 0} \dfrac{e^x-e^{x\cos x}}{x+\sin x}$

5 votes

How to solve $\int_0^\frac{\pi}{4} \frac{x \cos^2(2x)}{(1+\sin(2x)) (1+ \cos(2x))} dx$?

3 votes
Accepted

How do I solve this ODE? $\frac{1+2y'^2}{\sqrt{y(1+y'^2)}} = C$

3 votes
Accepted

How to integrate $\int_{0}^{1}\frac{x^{100}}{1+x}dx$?

3 votes
Accepted

Question about projection.

3 votes

Calculate $\int_C \frac{z^3 \, dz}{2z^4+1}$, $C$ is the circle $|z|=1$

3 votes

Consider the following recurrence, $a_n = \frac{1}{2}a_{n-1}+1$ where $a_1 = 1$. Guess a pattern for $a_n$ and prove it by induction.

3 votes

Computation of $\left.\dfrac{\text d^{100}}{\text dz^{100}}\cos(z^2)\right|_{z=0}$

3 votes

Can we prove that $\frac{1}{n}\sum_{k=1}^n a_k \rightarrow \frac{1}{2}$?

3 votes

Second order ODE solution approach

2 votes

How to untangle the ODE $\frac{dx}{dt} = c + \frac{px}{l_0 + pt}$?

2 votes

Evaluate integral of $\langle xz^2,x^2y-z^3,2xy+y^2z\rangle$ with divergence theorem

2 votes

Calculate $\int x^2\sqrt{a^2+x^2}dx$

2 votes
Accepted

Evaluation of $ \frac{1}{\pi} \int_{0}^{2\pi} \exp\left(-\sum_{k=1}^{K} x_k e^{-ik\pi\sin(\theta)}\right) d\theta$

2 votes

A $2D$ random walk with step size $1$ starts on the edge of a disk of radius $r$. What is probability that the walk will return to the disk?

2 votes

Third order term in Taylor Series

2 votes
Accepted

Distance between two planes parallel to two lines

2 votes

Finding the Volume of Region in Three-Dimensional Space.

2 votes

derivative of power series has the same convergence radius

2 votes
Accepted

Why do the constants $\gamma$, $\zeta(2)$ and $\zeta(3)$ appear in the values of $\Gamma''(1)$ and $\Gamma'''(1)$?

2 votes

Evaluate: $\int_{-1}^{1}\ln\left(\frac{1+t}{1-t}\right)\frac{1}{1-at}dt$

2 votes
Accepted

Determining condition of coplanarity

2 votes
Accepted

Applying linearity of a differential operator to solve ODE

2 votes

Is there an analytic continuation of the Legendre Chi function $\chi_2(z)$ for $z > 1$?

2 votes
Accepted

Find $\int_0^\pi \frac{8 \, d \theta}{5+2 \cos \theta}$

2 votes

Find the area enclosed by the curve $(x^2+y^2-1)^3-x^2y^3=0$

2 votes

Prove that $\sum_{n=0}^{\infty} \frac{2}{e^{(2n+1)U} - 1} = \sum_{n=1}^{\infty} \frac{1}{\sinh{(nU)}}$

1 vote

Fourier Transform (train of impulses)

1 vote
Accepted

Functional derivative of a function times its derivative