### Need help from an expert?

The world’s top online tutoring provider trusted by students, parents, and schools globally.

The integral of xe^xsin(x) is (x-1/2)e^xsin(x) - 1/2cos(x)e^x + C.

To solve this integral, we will use integration by parts. Let u = x and dv = e^xsin(x)dx. Then du/dx = 1 and v = -1/2cos(x)e^x - 1/2sin(x)e^x. Using the formula for integration by parts, we have:

∫xe^xsin(x)dx = uv - ∫vdu

= x(-1/2cos(x)e^x - 1/2sin(x)e^x) - ∫(-1/2cos(x)e^x - 1/2sin(x)e^x)dx

= (x-1/2)e^xsin(x) - 1/2cos(x)e^x + C

Therefore, the integral of xe^xsin(x) is (x-1/2)e^xsin(x) - 1/2cos(x)e^x + C.

Study and Practice for Free

Trusted by 100,000+ Students Worldwide

Achieve Top Grades in your Exams with our Free Resources.

Practice Questions, Study Notes, and Past Exam Papers for all Subjects!

The world’s top online tutoring provider trusted by students, parents, and schools globally.

Loading...

Loading...