← Integral Calculus
Mathematics · Cheatsheet

Integral Calculus

Chapter 1 · Foundations

📋 Reference · always available
Power rule (reverse)
∫xn dx=xn+1n+1+C  (n≠−1)\int x^n\,dx = \frac{x^{n+1}}{n+1} + C\;(n\neq-1)
Exponential / reciprocal
∫exdx=ex+C,∫1x dx=ln⁡∣x∣+C\int e^x dx = e^x + C,\quad \int \tfrac{1}{x}\,dx = \ln|x| + C
Definite integral (FTC)
∫abf(x) dx=F(b)−F(a)\int_a^b f(x)\,dx = F(b) - F(a)
+C reminder
Indefinite integrals always carry the constant of integration +C+C.
Power rule (integral)
∫xn dx=xn+1n+1+C  (n≠−1)\int x^n\,dx = \tfrac{x^{n+1}}{n+1}+C\;(n\neq-1)
+C and definite
∫abf=F(b)−F(a)\int_a^b f = F(b)-F(a)
Indefinite needs +C; definite gives a number (no C).
Standard integrals
∫ex=ex,  ∫1x=ln⁡∣x∣,  ∫cos⁡x=sin⁡x\int e^x = e^x,\;\int\tfrac1x = \ln|x|,\;\int\cos x = \sin x
Common trap
Don’t forget +C; ∫1/x = ln|x| (absolute value).