Thinking about a kind of heavy integral
04-25-2019, 01:22 PM (This post was last modified: 04-25-2019 01:30 PM by yangyongkang.)
Post: #1
 yangyongkang Member Posts: 51 Joined: Dec 2018
Thinking about a kind of heavy integral
Definite integral and indefinite integral can be said to be the core of calculus.I found that there is a kind of trigonometric integral, and XCAS can't do anything about it.

I will give the general form of it first.
Code:
int((a*sin(x)+b*cos(x))/(c+d*sin(2*x)+f*cos(2*x)), x)

Maple gives a general answer in the picture, and it can be seen that it is essentially necessary to solve a quadratic equation.

This type of indefinite integral can spawn many similar problems.
Code:
int(sin(x)/(2+sin(x)*cos(x)), x)

Code:
int(cos(x)/(2-sin(x)*cos(x)),x)

Code:
int((2sin(x)+3*cos(x))/(1+sin(x)*cos(x)),x)

Code:
int((sin(x)+cos(x))/(1-sin(x)*cos(x)),x)

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 Messages In This Thread Thinking about a kind of heavy integral - yangyongkang - 04-25-2019 01:22 PM RE: Thinking about a kind of heavy integral - parisse - 04-27-2019, 06:18 AM

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