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Nikunj's user avatar
Nikunj
  • Member for 8 years, 5 months
  • Last seen more than a month ago
19 votes

Calculate $\frac{1}{\sin(x)} +\frac{1}{\cos(x)}$ if $\sin(x)+\cos(x)=\frac{7}{5}$

19 votes
Accepted

A slightly problematic integral $\int{1/(x^4+1)^{1/4}} \, \mathrm{d}x$

10 votes
Accepted

Integrating $\int\frac{x^2-1}{(x^2+1)\sqrt{x^4+1}}\,dx$

9 votes

Solving for $x$ in $\tan(3x) \tan (2x)= 1$

8 votes
Accepted

arccot limit: $\sum_{r=1}^{\infty}\cot ^{-1}(r^2+\frac{3}{4})$

8 votes
Accepted

$\lim_{n\to \infty}\left(\frac{\sqrt[n]{a}+\sqrt[n]{b}}{2}\right)^n\stackrel{?}{=}\sqrt{ab}$

8 votes

Integrate $\int_0^1 \frac{x^2-1}{\left(x^4+x^3+x^2+x+1\right)\ln{x}} \mathop{dx}$

7 votes

Tangent plane to sphere

6 votes

Good idea to find below sum

6 votes
Accepted

How to integrate $\int\frac{\sqrt x}{\sqrt {1-x}}dx$?

6 votes
Accepted

Find $\lim_{x\to -\infty}\frac{3^{\sin x}+2x+1}{\sin x-\sqrt{x^2+1}}$

6 votes
Accepted

How can I prove $\int_{0}^{\infty}\frac{x^2+1}{(x^4+2ax^2+1)(x^s+1)} dx=\frac{π}{2\sqrt{2a+2}}$

6 votes
Accepted

Solution set of $3^{2x^2}-2.3^{{x^2}+x+6}+3^{2(x+6)}=0$

6 votes

Finding roots for algebraic equation

5 votes

How to integrate $ \int\frac{x-2}{(7x^2-36x+48)\sqrt{x^2-2x-1}}dx$?

5 votes

Prove that for all odd integer $n, n^{4}=1\pmod {16}$

5 votes
Accepted

A limits with substitution

5 votes
Accepted

If the largest positive integer is n such that $\sqrt{n - 100} + \sqrt{n + 100}$ is a rational no. , find the value of $\sqrt{n - 1}$ .

5 votes
Accepted

How to evaluate $\int ({x\sin^2{x}-x^2\sin x\cos x})dx$?

5 votes

The values of constants in the Equation.

5 votes

Calculate $\int_{-\pi}^{\pi} \frac{xe^{ix}} {1+\cos^2 {x}} dx$

5 votes
Accepted

A person has 8 friends and plans to invite 5 of them to a party, how many combinations are there if 2 of those friends must attend together?

4 votes

Find all pairs of prime numbers $p, q$ such that $p+q = 18(p−q)$.

4 votes
Accepted

Solution of ODE: $(f'(x))^2 - (f(x))^2+ 1 = 0$

4 votes
Accepted

Relation between $I_{k}$ and $I_{k+2}$

4 votes
Accepted

Is there an easy way of showing $8\cos^3(12^o)-6\cos(12^o)=\phi$?

4 votes

Evaluate $\int \frac{1}{\sqrt{x^2-1}}dx$ without using trigonometric substitutions

4 votes
Accepted

Did I answer these counting method questions correctly?

4 votes
Accepted

Limit calculation with Riemann integral

4 votes
Accepted

Geometric series $ar^n$ where $n \ne 1,2,3,4 \cdots$

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