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whatamidoing
  • Member for 1 year, 3 months
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8 votes

How to integrate $\int \frac{1}{x\ln x+x}dx$?

6 votes
Accepted

$\lim_{n\to\infty}\sqrt[n]{\int_0^1x^{\frac{n(n+1)}{2}}(1-x)(1-x^2)\cdots(1-x^n)dx}=\frac{1}{4}$

6 votes

Let $f : \{1, 2, 3, 4, 5, 6, 7\} \to \{1, 2, 3, 4, 5, 6, 7\}$, then number of functions with $f(f(f(x))) =x$.

5 votes
Accepted

Solve the integral $\int\frac{1}{4x^2 + 9} dx$

4 votes
Accepted

Solving the infinite series

4 votes

Can the integral be found without Feynman’s trick?

4 votes

Ellipse simultaneously touching and intersecting a parabola

4 votes
Accepted

If $f(x)=x^4+4x^3+26$, then find the number of solutions of $f(f(f(f(x))))=26$ is ____

3 votes
Accepted

If $4ax+3by+12c$ is normal to ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, then how are $c$, $a$, $e$ related?

3 votes
Accepted

Sum with Binomial Coefficients and Sine; $S=\sum_{k=0}^n \binom{n}{k} \sin(kx)$

3 votes
Accepted

Evaluate the integral $\int \frac{1 + x\cos(x)}{x(1-x^2e^{2\sin(x)})}\, dx$

3 votes
Accepted

Finding the general term of a sequence that $a_1 = 2\,$ and $\,a_{n+1} = (2\cdot a_n) + 5$.

3 votes

How would you do this integral?

3 votes

A particular linear recurrence relation

2 votes

Evaluating $\int_{0}^{\pi/2}\frac{1}{1+\tan^{101}x}dx$

2 votes

Are there any identities/techniques to simplify a a trigonometric function raised to a large power?

2 votes

Intergrate $\text{arccosh}(\sqrt{x^2 + 1})$ via hyperbolic substituation.

2 votes

Book recommendation for "intermediate level"problem book on calculus.

2 votes
Accepted

Find the limit of this large expression

2 votes

Discriminant of Quadratic Equation

2 votes

How to use substitution to integrate a function.

2 votes

For what $k$, are the roots of $p(x) = 4x^2 -2x +k=0$ in $(-1,1)$?

2 votes

Finding plane from from the projection of a line

1 vote

I'm having difficulties with finding angle between tangent drawn from origin to a circle

1 vote
Accepted

If $\sum_{p=0}^{2020}{\sin(2^p\theta)\sec(3^{p+1}\theta})=a\tan(b\theta)+c\tan(d\theta)$, find $ac,ad,cd,bd$

1 vote

Prove $\int_0^{\pi/4} \frac{x \cos 2x}{1-\sin x} \mathrm dx > \frac{1}{4}$

1 vote
Accepted

Calculate limit of a sum as an integral

1 vote

Derivative of $x \mapsto \left( 5 + x^2 \right)^{1/2} \left( x^3 + 1 \right)^{1/4}$

1 vote

Finding the radius of the circumcircle when orthocentre, circumcentre and a side is given

1 vote

Solving the summation of a binomial theorem