1 / | | / 3*x\ | \5*sin(2*x) + 14*E / dx | / 0
Integral(5*sin(2*x) + 14*E^(3*x), (x, 0, 1))
Integrate term-by-term:
The integral of a constant times a function is the constant times the integral of the function:
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
The integral of the exponential function is itself.
So, the result is:
Now substitute back in:
So, the result is:
The integral of a constant times a function is the constant times the integral of the function:
There are multiple ways to do this integral.
Let .
Then let and substitute :
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:
Now substitute back in:
The integral of a constant times a function is the constant times the integral of the function:
There are multiple ways to do this integral.
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
The integral of is when :
So, the result is:
Now substitute back in:
Let .
Then let and substitute :
The integral of is when :
Now substitute back in:
So, the result is:
So, the result is:
The result is:
Add the constant of integration:
The answer is:
/ | 3*x | / 3*x\ 5*cos(2*x) 14*e | \5*sin(2*x) + 14*E / dx = C - ---------- + ------- | 2 3 /
3 13 5*cos(2) 14*e - -- - -------- + ----- 6 2 3
=
3 13 5*cos(2) 14*e - -- - -------- + ----- 6 2 3
-13/6 - 5*cos(2)/2 + 14*exp(3)/3
Use the examples entering the upper and lower limits of integration.