What is the indefinite integral of [tex]6\sin(3t) \, dt[/tex]?

∫ 6 s in ( 3 t ) d t = − 2 cos ( 3 t ) + C
General Formulas and Concepts:
Calculus
Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: d x d ​ [ c f ( x )] = c ⋅ f ′ ( x )
Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals
[Indefinite Integrals] Integration Constant C

Integration Property [Multiplied Constant]: ∫ c f ( x ) d x = c ∫ f ( x ) d x
U-Substitution ;

Answered by Space | 2024-06-24

The indefinite integral of 6 sin ( 3 t ) d t is − 2 cos ( 3 t ) + C , where C is the integration constant. This result is obtained using substitution method. The process involves factoring out constants and using known integral formulas.
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Answered by Space | 2024-12-26