Table of Integrals

Power of x

$\int 𝑎 𝑑 𝑥 = 𝑎 𝑥 + 𝐶 \int 𝑥 𝑛 𝑑 𝑥 = 𝑥 𝑛 + 1 𝑛 + 1 + 𝐶 𝑛 \neq - 1 \int 1 𝑥 𝑑 𝑥 = l n | 𝑥 | + 𝐶$

Exponential and Logarithmic

$\int 𝑒 𝑥 𝑑 𝑥 = 𝑒 𝑥 + 𝐶 \int 𝑎 𝑥 𝑑 𝑥 = 𝑎 𝑥 l n 𝑎 + 𝐶 \int l n 𝑥 𝑑 𝑥 = 𝑥 l n 𝑥 - 𝑥 + 𝐶$

Trigonometric

$\int s i n 𝑥 𝑑 𝑥 = - c o s 𝑥 + 𝐶 \int c s c 𝑥 𝑑 𝑥 = l n | c s c 𝑥 - c o t 𝑥 | + 𝐶 \int c o s 𝑥 𝑑 𝑥 = s i n 𝑥 + 𝐶 \int s e c 𝑥 𝑑 𝑥 = l n | s e c 𝑥 + t a n 𝑥 | + 𝐶 \int t a n 𝑥 𝑑 𝑥 = l n | s e c 𝑥 | + 𝐶 \int c o t 𝑥 𝑑 𝑥 = l n | s i n 𝑥 | + 𝐶 = - l n | c o s 𝑥 | + 𝐶 \int s e c 2 𝑥 𝑑 𝑥 = t a n 𝑥 + 𝐶 \int c s c 2 𝑥 𝑑 𝑥 = - c o t 𝑥 + 𝐶 \int s e c 𝑥 t a n 𝑥 𝑑 𝑥 = s e c 𝑥 + 𝐶 \int c s c 𝑥 c o t 𝑥 𝑑 𝑥 = - c s c 𝑥 + 𝐶$

$\int s i n 2 𝑥 𝑑 𝑥 = \int (12 - 12 c o s 2 𝑥) 𝑑 𝑥 = 12 𝑥 - 14 s i n 2 𝑥 + 𝐶 \int c o s 2 𝑥 𝑑 𝑥 = \int (12 + 12 c o s 2 𝑥) 𝑑 𝑥 = 12 𝑥 + 14 s i n 2 𝑥 + 𝐶 \int t a n 2 𝑥 𝑑 𝑥 = \int (s e c 2 𝑥 - 1) 𝑑 𝑥 = t a n 𝑥 - 𝑥 + 𝐶$

Inverse Trigonometric

$\int 𝑑 𝑥 \sqrt 𝑎 2 - 𝑥 2 = s i n - 1 𝑥 𝑎 + 𝐶 \int 𝑑 𝑥 𝑎 2 + 𝑥 2 = 1 𝑎 t a n - 1 𝑥 𝑎 + 𝐶 \int 𝑑 𝑥 𝑥 \sqrt 𝑥 2 - 𝑎 2 = 1 𝑎 s e c - 1 ∣ 𝑥 𝑎 ∣ + 𝐶$

Hyperbolic

$R e m i n d e r : s i n h 𝑥 = 𝑒 𝑥 - 𝑒 - 𝑥 2 c o s h 𝑥 = 𝑒 𝑥 + 𝑒 - 𝑥 2 t a n h 𝑥 = s i n h 𝑥 c o s h 𝑥 c s c h 𝑥 = 1 s i n h 𝑥 s e c h 𝑥 = 1 c o s h 𝑥 c o t h 𝑥 = c o s h 𝑥 s i n h 𝑥$

$\int s i n h 𝑥 𝑑 𝑥 = c o s h 𝑥 + 𝐶 \int c s c h 𝑥 𝑑 𝑥 = l n ∣ t a n h 12 𝑥 ∣ + 𝐶 \int c o s h 𝑥 𝑑 𝑥 = s i n h 𝑥 + 𝐶 \int s e c h 𝑥 𝑑 𝑥 = t a n - 1 | s i n h 𝑥 | + 𝐶 \int t a n h 𝑥 𝑑 𝑥 = l n c o s h 𝑥 + 𝐶 \int c o t h 𝑥 𝑑 𝑥 = l n | s i n h 𝑥 | + 𝐶$

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