37 Do inequalities hold under differentiation? 16 Integration by substitution 14 Prove that the square of any given odd number gives a remainder of 1 when divided by 4 8 How to calculate this definite integral :- $\int_0^\pi \frac{x}{a^2\cos^2x + b^2\sin^2x} \,dx$? 8 Six x’s has to be placed in the squares in the adjacent figure, such that each row contains at least one x. This can be done in

### Reputation (15,582)

 +10 Prove that $\sin n\theta=n\sin \theta-\frac{n(n^2-1)}{3!}\sin^3\theta+\frac{n(n^2-1)(n^2-3^2)}{5!}\sin^5\theta+\cdots$ +10 Formula for the general term of the Taylor series of $\tan(x)$ at $x = 0$ +10 Finding maximum value of an expression $3a+4b$ where $(a,b)$ lies on unit circle. -2 How to integrate $\cos(z)~dz$?

### Questions (227)

 11 If $\int_1^ \infty \frac {x^3+3}{x^6(x^2+1)} \, \mathrm d x=\frac{a+b\pi}{c}$, then find $a,b,c$. 11 Computing $\int_0^\infty\frac{1}{(1+x^{2015})(1+x^2)}$ [duplicate] 11 Factorial Calculation for Non-Integers? 11 confusion about permutation 10 Value of this convergent series: $\frac{1}{3!}+\frac2{5!}+\frac3{7!}+\frac{4}{9!}+\cdots$

### Tags (213)

 239 calculus × 201 70 derivatives × 63 150 integration × 118 67 inequality × 33 97 algebra-precalculus × 123 64 limits × 69 90 trigonometry × 139 56 definite-integrals × 62 75 combinatorics × 90 50 sequences-and-series × 67

### Bookmarks (59)

 17 Need help with $\int_0^\infty\arctan\left(e^{-x}\right)\,\arctan\left(e^{-2x}\right)\,dx$ 13 Non-Circular Proof of $\lim_{x \to 0} \frac{\sin x}{x} = 1$ 10 How to prove $\prod _{a=0}^{9}\prod_{b=0}^{100}\prod_{c=0}^{100}(w^a+z^b+z^c)\equiv?\pmod {101}$ 9 Digit-Sum of a Number. 8 If $f(f(x))=x^2-x+1$, what is $f(0)$?

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