1 / | | 5 | x *cos(x) dx | / 0
Integral(x^5*cos(x), (x, 0, 1))
Use integration by parts:
Let and let .
Then .
To find :
The integral of cosine is sine:
Now evaluate the sub-integral.
Use integration by parts:
Let and let .
Then .
To find :
The integral of sine is negative cosine:
Now evaluate the sub-integral.
Use integration by parts:
Let and let .
Then .
To find :
The integral of cosine is sine:
Now evaluate the sub-integral.
Use integration by parts:
Let and let .
Then .
To find :
The integral of sine is negative cosine:
Now evaluate the sub-integral.
Use integration by parts:
Let and let .
Then .
To find :
The integral of cosine is sine:
Now evaluate the sub-integral.
The integral of a constant times a function is the constant times the integral of the function:
The integral of sine is negative cosine:
So, the result is:
Add the constant of integration:
The answer is:
/ | | 5 5 2 3 4 | x *cos(x) dx = C + 120*cos(x) + x *sin(x) - 60*x *cos(x) - 20*x *sin(x) + 5*x *cos(x) + 120*x*sin(x) | /
-120 + 65*cos(1) + 101*sin(1)
=
-120 + 65*cos(1) + 101*sin(1)
-120 + 65*cos(1) + 101*sin(1)
Use the examples entering the upper and lower limits of integration.