query: if $f(x) = \int_{t=1}^{t=x^2} t\sin^2(t)\operatorname d\!t$ then $\frac{\operatorname d\!f(x)}{\operatorname d\!x}=?$
positive_passages.docid: 20904
positive_passages.text: Finding derivative of this integral function.
negative_passages.docid: 8829
negative_passages.text: How to prove $\int_{-\infty}^{+\infty} f(x)dx = \int_{-\infty}^{+\infty} f\left(x - \frac{1}{x}\right)dx?$
negative_passages.docid: 132124
negative_passages.text: $\int_{0}^{\infty}\frac{x}{x^3+1}dx$ =?
negative_passages.docid: 133990
negative_passages.text: How prove this $\int_{a}^{b}f(x)dx=\frac{1}{2}(b-a)[f(a)+f(b)]-\frac{1}{12}(b-a)^3f''(\xi)$
negative_passages.docid: 84420
negative_passages.text: When is $\sin(x) = \cos(x)$?
negative_passages.docid: 129902
negative_passages.text: If $f(x)=x+\int_{0}^{1}[xy^2+x^2y]f(y)dy$ where $x$ and$y$ are independent variable.Find $f(x).$
negative_passages.docid: 127558
negative_passages.text: If $f(x)=x-\int^{\frac{\pi}{2}}_0f(x)\sin(x)dx$ find the explicit function for $f(x)$ in its simplest form
negative_passages.docid: 156215
negative_passages.text: Integral $\int\frac{2x^2}{2x\cos(2x)+(x^2-1)\sin(2x)} \mathrm d x$
negative_passages.docid: 106853
negative_passages.text: Find all functions: $\left ( \int \frac{dx}{f(x)} \right )\left ( \int f(x)dx \right )=c$
negative_passages.docid: 58901
negative_passages.text: Why is every such function constant: $f(x)=f(x^2)$ for $x \in [0,1]$?
negative_passages.docid: 63750
negative_passages.text: let $f(\frac{x}{3})+f(\frac{2}{x})=\frac{4}{x^2}+\frac{x^2}{9}-2$ then find $f(x)$
negative_passages.docid: 133682
negative_passages.text: Prove that if $f(t)$ satisfies $f(t)=f'(t)$, then $f(t+s)=f(t)f(s)$ for all $t,s\in R$ without using the fact that $f(t)=c\cdot e^t$.
negative_passages.docid: 55175
negative_passages.text: Is the function $f(x) = x^2 - 2x$ one-to-one?
negative_passages.docid: 53024
negative_passages.text: $f(x)f(1/x)=f(x)+f(1/x)$
negative_passages.docid: 97253
negative_passages.text: How prove $e^x|f(x)|\le 2$ if $f(x)=\int_{x}^{x+1}\sin{(e^t)}dt$
negative_passages.docid: 151519
negative_passages.text: If $f(f(x))=x^2-x+1$, what is $f(0)$?
negative_passages.docid: 112707
negative_passages.text: Must $Q^\mathsf{T}Q = I$ if $(Qx)^\mathsf{T}(Qx) = x^\mathsf{T}x$