\begin
Discover why 18 million people worldwide trust Overleaf with their work.
\documentclass[avery5371,grid]{flashcards}
% -------------------
% Packages
% -------------------
\usepackage{amsmath,geometry}
\geometry{bindingoffset=0.0cm,hratio=1:1}
\usepackage[bitstream-charter]{mathdesign}
\usepackage[T1]{fontenc}
% -------------------
% Card Option
% -------------------
\cardfrontstyle{empty}
\cardbackstyle{empty}
% -------------------
% Content
% -------------------
\begin{document}
\begin{flashcard}{\large \vspace*{\fill} \[ \int\; \text{ \normalfont constant} \;dx \] \vspace*{\fill} }{\large \vspace*{\fill} \[ \text{constant } \cdot x + C \] \vspace*{\fill} }\end{flashcard}
\begin{flashcard}{\large \vspace*{\fill} \[ \int\; x^n \;dx \] \vspace*{\fill} }{\large \vspace*{\fill} \[ \dfrac{x^{n+1}}{n+1} + C ; \quad n \neq -1 \] \vspace*{\fill} }\end{flashcard}
\begin{flashcard}{\large \vspace*{\fill} \[ \int\; \dfrac{1}{x} \;dx \] \vspace*{\fill} }{\large \vspace*{\fill} \[ \ln|x| + C \] \vspace*{\fill} }\end{flashcard}
\begin{flashcard}{\large \vspace*{\fill} \[ \int\; \sin x \;dx \] \vspace*{\fill} }{\large \vspace*{\fill} \[ -\cos x + C \] \vspace*{\fill} }\end{flashcard}
\begin{flashcard}{\large \vspace*{\fill} \[ \int\; \cos x \;dx \] \vspace*{\fill} }{\large \vspace*{\fill} \[ \sin x + C \] \vspace*{\fill} }\end{flashcard}
\begin{flashcard}{\large \vspace*{\fill} \[ \int\; \sec^2 x \;dx \] \vspace*{\fill} }{\large \vspace*{\fill} \[ \tan x + C \] \vspace*{\fill} }\end{flashcard}
\begin{flashcard}{\large \vspace*{\fill} \[ \int\; \sec x \, \tan x \;dx \] \vspace*{\fill} }{\large \vspace*{\fill} \[ \sec x + C \] \vspace*{\fill} }\end{flashcard}
\begin{flashcard}{\large \vspace*{\fill} \[ \int\; \csc^2 x \;dx \] \vspace*{\fill} }{\large \vspace*{\fill} \[ -\cot x + C \] \vspace*{\fill} }\end{flashcard}
\begin{flashcard}{\large \vspace*{\fill} \[ \int\; \csc x \, \cot x \;dx \] \vspace*{\fill} }{\large \vspace*{\fill} \[ -\csc x + C \] \vspace*{\fill} }\end{flashcard}
\begin{flashcard}{\large \vspace*{\fill} \[ \int\; \tan x \;dx \] \vspace*{\fill} }{\large \vspace*{\fill} \[ \ln|\sec x| + C \] \vspace*{\fill} }\end{flashcard}
\begin{flashcard}{\large \vspace*{\fill} \[ \int\; e^x \;dx \] \vspace*{\fill} }{\large \vspace*{\fill} \[ e^x + C \] \vspace*{\fill} }\end{flashcard}
\begin{flashcard}{\large \vspace*{\fill} \[ \int\; a^x \;dx \] \vspace*{\fill} }{\large \vspace*{\fill} \[ \dfrac{a^x}{\ln a} + C \] \vspace*{\fill} }\end{flashcard}
\begin{flashcard}{\large \vspace*{\fill} \[ \int\; \ln x \;dx \] \vspace*{\fill} }{\large \vspace*{\fill} \[ x\ln x - x + C \] \vspace*{\fill} }\end{flashcard}
\begin{flashcard}{\large \vspace*{\fill} \[ \int\; \dfrac{1}{1+x^2} \;dx \] \vspace*{\fill} }{\large \vspace*{\fill} \[ \arctan x + C \] \vspace*{\fill} }\end{flashcard}
\begin{flashcard}{\large \vspace*{\fill} \[ \int\; \dfrac{1}{\sqrt{1-x^2}} \;dx \] \vspace*{\fill} }{\large \vspace*{\fill} \[ \arcsin x + C \] \vspace*{\fill} }\end{flashcard}
\begin{flashcard}{\large \vspace*{\fill} \[ \int\; \dfrac{1}{x \sqrt{x^2-1}} \;dx \] \vspace*{\fill} }{\large \vspace*{\fill} \[ \sec^{-1}|x| + C \] \vspace*{\fill} }\end{flashcard}
\begin{flashcard}{\large \vspace*{\fill} \[ \int\; u \, v' \;dx \] \vspace*{\fill} }{\large \vspace*{\fill} \[ uv \;-\; \int\; v u' \; dx \] \vspace*{\fill} }\end{flashcard}
\begin{flashcard}{\large \vspace*{\fill} \[ \int_a^b\; u \, v' \;dx \] \vspace*{\fill} }{\large \vspace*{\fill} \[ (uv)\big|_a^b \;-\; \int_a^b\; v u' \; dx \] \vspace*{\fill} }\end{flashcard}
\begin{flashcard}{\large \vspace*{\fill} \[ \int\; uv \;dx \neq \] \vspace*{\fill} }{\large \vspace*{\fill} \[ \int\; uv \;dx \neq \int u \;dx \cdot \int v \;dx \] \vspace*{\fill} }\end{flashcard}
\begin{flashcard}{\large \vspace*{\fill} \[ \int\; \dfrac{u}{v} \;dx \neq \] \vspace*{\fill} }{\large \vspace*{\fill} \[ \int\;\dfrac{u}{v} \;dx \neq \dfrac{\int u \; dx}{\int v \;dx} \] \vspace*{\fill} }\end{flashcard}
\end{document}