Question

4. Write a MatLab program that calculates the following indefinite integrals. The program should use pretty() to display both the original integrand and the integrated result, and also us

Answer 1

MATLAB code to find the integration of three functions:

clc
clear all
syms x a b c
fprintf('Integrate \n')
f1=(sin(3*x))/(cos(x))^5;
pretty(f1)
fprintf('Result1 = \n')
Result1=int(f1);
pretty(Result1)
fprintf('Result1 after simlification using simplify() command \n')
pretty(simplify(Result1));
fprintf('Integrate \n')
f2=x/((a+c*x^2)^(5/2));
pretty(f2)
fprintf('Result2 = \n')
Result2=int(f2);
pretty(Result2)
fprintf('Result2 after simlification using simplify() command \n')
pretty(simplify(Result2))
fprintf('Integrate \n')
f3=sin(x)/(a*cos(x)+b*sin(x))^2;
pretty(f3)
fprintf('Result3 = \n')
Result3=int(f2);
pretty(Result3)
fprintf('Result3 after simlification using simplify() command \n')
pretty(simplify(Result3))

MATLAB OUTPUT:

Integrate
sin(3 x)
--------
5
cos(x)

Result1 =
2
8 cos(x) - 1
-------------
4
4 cos(x)

Result1 after simlification using simplify() command
2
8 cos(x) - 1
-------------
4
4 cos(x)

Integrate
x
-------------
2 5/2
(c x + a)

Result2 =
1
- -----------------
2 3/2
3 c (c x + a)

Result2 after simlification using simplify() command
1
- -----------------
2 3/2
3 c (c x + a)

Integrate
sin(x)
----------------------
2
(a cos(x) + b sin(x))

Result3 =
1
- -----------------
2 3/2
3 c (c x + a)

Result3 after simlification using simplify() command
1
- -----------------
2 3/2
3 c (c x + a)

None of results simplify using simplify() command.