Further Calculus

∫ (ax + b)ⁿ dx

1/a * (ax + b)ⁿ⁺¹/ (n+1) + c

∫ (a²+ x²)^-1 dx

1/a * arctan(x/a) + c

∫ (a²+ x²)^-1/2 dx

arcsin(x/a) + c

(a² - x²)^1/2

Trig Substitution and Identity

x = a sin θ

1 - sin²θ = cos²θ

(a² + x²)^1/2

Trig Substitution and Identity

x = a tan θ

1 + tan²θ = sec²θ

(x² - a²)^1/2

Trig Substitution and Identity

x = a sec θ

sec²θ - 1 = tan²θ