Rajesh K Singh
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### Questions (98)

 21 If $a$, $a+2$ and $a+4$ are prime numbers then, how can one prove that there is only one solution for $a$? 9 Integrating $\int_0^\infty\frac{1}{1+x^6}dx$ 7 factorise, $x^3-13x^2+32x+20$ 7 Prove that $(n+\sqrt{n^2 -1})^k$ will always be of the form$(t+\sqrt{t^2 -1})$ where $n$, $k$, $t$ are natural numbers 6 How to integrate, $\int_{0}^{\pi/2}\sin (\tan\theta) \mathrm{d\theta}$?

### Reputation (1,317)

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 3 What is the remainder when $25^{889}$ is divided by 99? 2 Integrating $\int \sqrt{\frac{1+x}{x}}dx$ 2 I know that, $S_{2n}+4S_{n}=n(2n+1)^2$. Is there a way to find $S_{2n}$ or $S_{n}$ by some mathematical process with just this one expression? 2 how can one solve for $x$, $x =\sqrt{2+\sqrt{2+\sqrt{2\cdots }}}$ 2 How to integrate $\frac{1}{\sqrt{1+x^2}}$ using substitution?

### Tags (76)

 5 algebra-precalculus × 23 2 substitution 5 elementary-number-theory × 14 2 indefinite-integrals 3 integration × 13 2 divisibility 3 recurrence-relations × 4 1 functions × 9 2 nested-radicals × 2 1 differential-equations × 8

### Accounts (17)

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