query: Find ab if $\int \:\frac{dx}{\left(e^x+1\right)}=ax+bln\left(e^x+1\right)+C$
positive_passages.docid: 18732
positive_passages.text: How do I evaluate $\int \frac{\mathrm{d}x}{e^x + 1} $?
negative_passages.docid: 69653
negative_passages.text: Inequality $\left(a-1+\frac{1}b\right)\left(b-1+\frac{1}c\right)\left(c-1+\frac{1}a\right)\leq1$
negative_passages.docid: 140290
negative_passages.text: Solving $AB - BA = C$
negative_passages.docid: 122361
negative_passages.text: Evaluate $\int_0^1\left(\frac{1}{\ln x} + \frac{1}{1-x}\right)^2 \mathrm dx$
negative_passages.docid: 140386
negative_passages.text: Integrate $\int {\dfrac{x^2+\left(n-1\right)n}{\left(x\sin x+n\cos x\right)^2}}dx $
negative_passages.docid: 157068
negative_passages.text: Prove that $\left (\frac{1}{a}+1 \right)\left (\frac{1}{b}+1 \right)\left (\frac{1}{c}+1 \right) \geq 64.$
negative_passages.docid: 16382
negative_passages.text: Find $a$ such that $(x+a)(x+1991)+1=(x+b)(x+c)$ with $a,b,c\in\Bbb Z$
negative_passages.docid: 69673
negative_passages.text: Prove that $\left (\frac{a^2 + b^2 +c^2}{a+b+c} \right) ^ {(a+b+c)} > a^a b^b c^c$
negative_passages.docid: 33240
negative_passages.text: $ \frac{1}{a^{2} + b^{2} + 1} + \frac{1}{b^{2}+c^{2}+1} + \frac{1}{c^{2} + a^{2} + 1} \ge 1 $, prove $ab + bc + ca \le 3$
negative_passages.docid: 13220
negative_passages.text: find the minimum value of $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}$
negative_passages.docid: 53518
negative_passages.text: Integrating : $\int_0^1 {\frac {x^a-x^b} {\ln x} dx}$
negative_passages.docid: 5034
negative_passages.text: A closed form of $\int_0^1\frac{\ln\ln\left({1}/{x}\right)}{x^2-x+1}\mathrm dx$
negative_passages.docid: 21390
negative_passages.text: How to integrate $\int_0^{\infty} \frac{e^{ax} - e^{bx}}{(1 + e^{ax})(1+ e^{bx})}dx$ where $a,b > 0$.
negative_passages.docid: 143734
negative_passages.text: Evaluating $\int \frac{\sin\left(x\right)}{1+x^2}dx$
negative_passages.docid: 26444
negative_passages.text: How can I integrate $\ln \left( x+\sqrt{1+x^2} \right) $?
negative_passages.docid: 72351
negative_passages.text: Applying integral substitution rule to $ \int \frac{mx+n}{ax+b} \mathrm{d}x$
negative_passages.docid: 126931
negative_passages.text: Find $f(x)$ such that $f(x)+f\left(\frac{1}{x}\right)=f(x)\cdot f\left(\frac{1}{x}\right)$