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e^xsin(x)−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy

Exercise

∫0a(exsin⁡(x))dx\int_0^a\left(e^x\sin\left(x\right)\right)dx

Step-by-step Solution

Learn how to solve integration by parts problems step by step online. Integrate the function e^xsin(x) from 0 to a. We can solve the integral \int e^x\sin\left(x\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.
Integrate the function e^xsin(x) from 0 to a

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Final answer to the exercise

12(easin⁡(a)+1−eacos⁡(a))\frac{1}{2}\left(e^a\sin\left(a\right)+1-e^a\cos\left(a\right)\right)

Try other ways to solve this exercise

  • Choose an option
  • 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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Main Topic: Integration by Parts

Integration by parts is an integration method that relates the integral of a product of two or more functions to the integral of their derivative and antiderivative.

Related Topics

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