query: How do you differentiate the integral from $ \int_{e^{-x}}^{e^x} \sqrt{1+t^2}\,dt$
positive_passages.docid: 25162
positive_passages.text: Differentiating Definite Integral
negative_passages.docid: 109561
negative_passages.text: Find $F'(x)$ if $F(x) = \displaystyle \int_{0}^x xf(t)dt$.
negative_passages.docid: 51971
negative_passages.text: How to evaluate the integral $\int e^{x^3}dx $
negative_passages.docid: 21616
negative_passages.text: Calculate integral $\int_{-1}^{1} (1-x^2)^n dx $
negative_passages.docid: 134871
negative_passages.text: Using definition of derivative to differentiate $f(x)= \sqrt{x}+1$
negative_passages.docid: 109385
negative_passages.text: Evaluating the integral $\int_{-\ln 2}^{\ln 2} e^{-x}(\sin x+x)^{1/3}dx$
negative_passages.docid: 67608
negative_passages.text: Integration of $1/(x^2+x\sqrt{x})$
negative_passages.docid: 53224
negative_passages.text: $e^{-x}f(x)=2+ \int_0^x\sqrt{t^4+1}dt$ function for finding the inverse
negative_passages.docid: 144023
negative_passages.text: Indefinite integral which is not differentiable
negative_passages.docid: 145403
negative_passages.text: Stuck in integration: $\int {\frac{dx}{( 1+\sqrt {x})\sqrt{(x-{x}^2)}}}$
negative_passages.docid: 54735
negative_passages.text: What is the closed form of $\int e^{x^2} \, dx$?
negative_passages.docid: 36128
negative_passages.text: Using differentiation for computing $\int_{0}^{1}\frac{\arctan(ax)}{x\sqrt{1-x^2}}\,dx$
negative_passages.docid: 45803
negative_passages.text: Integral of Derivative squared
negative_passages.docid: 8642
negative_passages.text: Calculate $ \int_{-2}^{0} \frac{x}{\sqrt{e^x+(x+2)^2}} dx $
negative_passages.docid: 28053
negative_passages.text: Integral of $\sin(e^t)dt$
negative_passages.docid: 151127
negative_passages.text: Confirm that $\int_{0}^{\infty}t^{-1}\sin t dt=\pi/2$
negative_passages.docid: 129892
negative_passages.text: show $\int_0^{\infty} \frac{x\sin ax}{x^2+t^2}dx = \frac{\pi}{2}e^{-at}$