integrate (or int) computes a primitive or a definite integral. A difference between the two commands is that if you input quest() just after the evaluation of integrate, the answer is written with the ∫ symbol.
integrate (or int or Int) takes one, two or four arguments.
^
2)^
3/3^
2,t)^
3/3^
2,x,1,2)Int is the inert form of integrate, it prevents evaluation
for example to avoid a symbolic computation that might not be
successful if you just want a numeric
evaluation.
Input :
^
2),x,0,1))or :
^
2),x,0,1))Output :
Exercise 1
Let
f(x)= |
| +ln( |
| ) |
Find a primitive of f.
Input :
^
2-1)+ln((x+1)/(x-1)))Output :
^
2-1)+1/2*log(2*x^
2/2-1)Or define the function f, input :
^
2-1)+ln((x+1)/(x-1))then input :
Output of course the same result.
Warning
For Xcas, log is the natural logarithm (like ln),
as log10 is 10-basis logarithm
Exercise 2
Compute :
∫ |
| dx |
Input :
^
6+2*x^
4+x^
2))Output :
^
2+2)/(-(2*(x^
3+x)))+-3/2*atan(x))Exercise 3
Compute :
∫ |
| dx |
Input :
Output :
^
2-3)+1/12*log((tan(x/2))^
2))*2