Final answer to the problem
$-\frac{3}{24050}e^{-500t}\cos\left(2000t\right)+\frac{6}{12025}e^{-500t}\sin\left(2000t\right)+C_0$
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Step-by-step Solution
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- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
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1
Simplifying
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$\int30e^{-500t}\cos\left(2000t\right)dt$
Learn how to solve problems step by step online. Find the integral int(5e^(-500t)*6cos(2000t))dt. Simplifying. The integral of a function times a constant (30) is equal to the constant times the integral of the function. We can solve the integral \int e^{-500t}\cos\left(2000t\right)dt by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify or choose u and calculate it's derivative, du.
Final answer to the problem
$-\frac{3}{24050}e^{-500t}\cos\left(2000t\right)+\frac{6}{12025}e^{-500t}\sin\left(2000t\right)+C_0$
