1 / | | (sin(x + y) + x*cos(x + y)) dx | / 0
Integral(sin(x + y) + x*cos(x + y), (x, 0, 1))
Integrate term-by-term:
Use integration by parts:
Let and let .
Then .
To find :
Let .
Then let and substitute :
The integral of cosine is sine:
Now substitute back in:
Now evaluate the sub-integral.
Let .
Then let and substitute :
The integral of sine is negative cosine:
Now substitute back in:
Let .
Then let and substitute :
The integral of sine is negative cosine:
Now substitute back in:
The result is:
Add the constant of integration:
The answer is:
/ | | (sin(x + y) + x*cos(x + y)) dx = C + x*sin(x + y) | /
sin(1 + y)
=
sin(1 + y)
sin(1 + y)
Use the examples entering the upper and lower limits of integration.