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Exercise

∫e−rx2tsinwrx dx\int e^{-\frac{rx}{2t}}sinwrx\:dx

Step-by-step Solution

Learn how to solve integrals involving logarithmic functions problems step by step online. Find the integral int(e^((-rx)/(2t))sin(wrx))dx. We can solve the integral \int e^{\frac{-rx}{2t}}\sin\left(wrx\right)dx 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. Now, identify dv and calculate v. Solve the integral to find v.
Find the integral int(e^((-rx)/(2t))sin(wrx))dx

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Final answer to the exercise

−2tsin⁡(wrx)−4t2wcos⁡(wrx)rerx2t(4t2w2+1)+C0\frac{-2t\sin\left(wrx\right)-4t^2w\cos\left(wrx\right)}{re^{\frac{rx}{2t}}\left(4t^2w^2+1\right)}+C_0

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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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∫e−rx2t sinwrx dx
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