{"A standard special-function form uses the error function, erf.":"標準特殊函數形式使用誤差函數erf。","A standard special-function form uses the logarithmic integral, li.":"標準特殊函數形式使用對數積分li。","A standard special-function form uses the sine integral, Si. Definite integration uses the continuous value 1 at zero.":"標準特殊函數形式使用正弦積分Si。定積分在零點使用連續值1。","Absolute-value rule, away from zero":"絕對值法則，避開零點","Adaptive Simpson numerical integration.":"自適應Simpson數值積分。","Angles":"角度","Antiderivative":"反導函數","Calculate":"計算","Calculating…":"計算中…","Chain rule":"鏈鎖律","Choose a definite integral and enter finite bounds for a numerical result.":"選擇定積分，並輸入有限上下限以取得數值結果。","Choose a derivative order from 1 to 5.":"選擇1到5階的導數階數。","Choose a single letter other than e or i as the variable.":"選擇單一字母作為變數，但不能使用e或i。","Combine the antiderivatives":"合併反導函數","Complete the square":"配方法","Constant multiple rule":"常數倍法則","Constant rule":"常數法則","Copy antiderivative":"複製反導函數","Copy derivative":"複製導數","Cross-check passed at seven random domain points. Numerical agreement is not a proof.":"已在七個隨機定義域點通過交叉檢查。數值一致並不代表證明成立。","Definite integral":"定積分","Degrees":"度","Degrees scale trig inputs by π/180 and inverse trig outputs by 180/π. These factors also appear in the calculus.":"度數會將三角函數輸入乘以π/180，並將反三角函數輸出乘以180/π。這些因子也會出現在微積分中。","Derivative calculator":"導數計算機","Derivative of order {0}":"{0}階導數","Derivative order":"導數階數","Differentiate the candidate and check seven random domain points":"對候選結果微分，並檢查七個隨機定義域點","Enter finite bounds. Improper integrals and infinite bounds are not supported.":"請輸入有限上下限。不支援廣義積分和無限上下限。","Estimated quadrature error: {0}. This is an estimate, not a rigorous bound.":"估計積分誤差：{0}。這是估計值，不是嚴格的界限。","Evaluate at (optional)":"計算指定點的值（選填）","Evaluated from the verified antiderivative and checked numerically.":"已根據驗證過的反導函數計算，並完成數值檢查。","Expected a closing parenthesis or absolute-value bar.":"預期為右括號或絕對值符號。","Expected a number, variable or function.":"預期為數字、變數或函數。","Exponential and trigonometric product":"指數與三角函數乘積","Exponential rule":"指數法則","Expression":"運算式","Fifth":"第五階","First":"第一階","For example, pi/2":"例如，pi/2","Fourth":"第四階","Function and first derivative plot":"函數與一階導數圖","General power rule":"一般冪次法則","Graphing calculator":"繪圖計算機","Integral calculator":"積分計算機","Integrand with shaded definite area":"帶有陰影定積分面積的被積函數","Integration by parts":"分部積分","Inverse trigonometric rule":"反三角函數法則","Library antiderivative; differentiate to verify":"函式庫反導函數；透過微分進行驗證","Linearity":"線性法則","Loading maths…":"正在載入數學運算…","Logarithm rule":"對數法則","Logarithmic rule":"對數法則","Lower bound":"下限","Maths rendering could not load.":"無法載入數學式呈現功能。","No closed form found.":"找不到封閉形式。","No elementary antiderivative exists.":"不存在初等反導函數。","Numerical integration did not converge within the error and evaluation limits.":"數值積分在誤差與計算次數限制內未收斂。","Order {0}":"{0}階","Parsed input":"解析後的輸入","Partial-fraction decomposition with numerically checked coefficients":"係數經數值檢查的部分分式分解","Polynomial long division":"多項式長除法","Position {0}.":"位置{0}。","Power reduction":"降冪","Power rule":"冪次法則","Product rule":"乘積法則","Quadratic equation solver":"二次方程式解算器","Quadratic radical formula":"二次方程式根公式","Quotient rule":"商法則","Radians":"弧度","Real-valued expressions in one variable. Up to 512 characters. Infinite bounds, singular intervals and general piecewise expressions are unsupported.":"單一變數的實值運算式。最多512個字元。不支援無限上下限、奇異區間和一般分段運算式。","Related maths tools":"相關數學工具","Repeated integration by parts table":"重複分部積分表","Rules apply on the original real domain. Absolute values are differentiated piecewise away from their zeros; higher derivatives at corners are not inferred from simplification.":"法則適用於原始實數定義域。絕對值會在避開零點的區段中分段微分；不會根據化簡結果推導折角處的高階導數。","Scientific calculator":"科學計算機","Second":"第二階","Shading shows the signed area. Sampled plot; gaps and steep values are omitted.":"陰影顯示帶符號面積。這是取樣繪圖；缺口與陡峭值會省略。","Solid: f. Dashed: f′. Sampled plot; gaps and steep values are omitted.":"實線：f。虛線：f′。這是取樣繪圖；缺口與陡峭值會省略。","Step-by-step working":"逐步計算過程","Substitution":"代換","Sum and difference rule":"和與差法則","Symbolic cross-check passed: the difference simplifies to zero.":"已通過符號交叉檢查：差值可化簡為零。","The antiderivative was found by the library. This outline lists only patterns recognised independently; it is not a trace of the library’s method.":"反導函數由函式庫求得。本概要只列出獨立辨識出的模式，不是函式庫方法的運算追蹤。","The derivative is undefined at this point.":"導數在此點未定義。","The expression is not defined as a finite real number here.":"運算式在此處未定義為有限實數。","The expression is too large. Use at most 512 characters, 160 nodes and 32 nesting levels.":"運算式過大。最多可使用512個字元、160個節點和32層巢狀。","The interval contains a domain gap, singularity, or a domain that could not be certified.":"此區間包含定義域缺口、奇異點，或無法確認的定義域。","The rule engine and library did not agree. The library result is shown; the working below is the rule engine’s attempt.":"規則引擎與函式庫的結果不一致。畫面顯示函式庫結果；下方計算過程是規則引擎的嘗試。","The symbolic calculation could not be completed. Try a smaller expression.":"無法完成符號計算。請嘗試較小的運算式。","These steps show the rules used to construct the antiderivative. The result also passed derivative-back numerical verification.":"這些步驟顯示建立反導函數所使用的法則。結果也通過了微分回代的數值驗證。","Third":"第三階","This character or name is not supported.":"不支援此字元或名稱。","Trigonometric rule":"三角函數法則","Try 2x, 3sin(x), e^x, ln(x), sqrt(x), |x| or log_2(x). Use parentheses after function names.":"請嘗試2x、3sin(x)、e^x、ln(x)、sqrt(x)、|x|或log_2(x)。函數名稱後請使用括號。","Unexpected input after the expression.":"運算式後有非預期的輸入。","Upper bound":"上限","Value at the chosen point: {0}":"指定點的值：{0}","Variable":"變數","Variable rule":"變數法則","Verified by differentiation at seven random domain points. Numerical agreement is not a proof. The constant may differ between disconnected intervals.":"已在七個隨機定義域點透過微分完成驗證。數值一致並不代表證明成立。常數在不連通區間之間可能不同。","Working outline":"計算過程概要"}