Formulaes of integral

Power Rule:    ∫x^n dx = (x^(n+1))/(n+1) + C, where "n" is a constant different from -1, and "C" is the constant of integration.

Exponential Rule: ∫e^x dx = e^x + C.

Trigonometric Integrals:

∫sin(x) dx = -cos(x) + C.
∫cos(x) dx = sin(x) + C.
∫sec^2(x) dx = tan(x) + C.
∫csc^2(x) dx = -cot(x) + C.

Inverse Trigonometric Integrals:

∫(1/√(1-x^2)) dx = arcsin(x) + C.
∫(1/(1+x^2)) dx = arctan(x) + C.

Integration by Parts:  ∫u dv = uv - ∫v du, where "u" and "v" are differentiable functions of "x."

Integration of Rational Functions:  Integrals of the form ∫(P(x)/Q(x)) dx, where P(x) and Q(x) are polynomials, can be solved using partial fraction decomposition.

Integration of Trigonometric Products: Integrals involving products of trigonometric functions can be solved using trigonometric identities and manipulation.

Substitution Rule: Also known as the u-substitution method, this involves substituting a new variable to simplify the integral. ∫f(g(x))g'(x) dx = ∫f(u) du, where "u" = g(x).

Definite Integral of Even and Odd Functions: If "f(x)" is an even function, ∫[-a to a] f(x) dx = 2∫[0 to a] f(x) dx. If "f(x)" is an odd function, ∫[-a to a] f(x) dx = 0.

Integration of Hyperbolic Functions: Similar to trigonometric functions, hyperbolic functions have their own set of integrals and identities.








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