Please give cos 4 x dx a more concise and convenient way than my solution urgently

Then put cos

4x is unwrapped with a trigonometric formula.

Replace all with additive.

Because I can't see your mathematical symbols clearly, I can't help you.

A function that can be stored in zhà no

definite integrals, which do not belong to the existence of definite integrals; It is also possible to have definite integrals without indefinite integrals. For a continuous function, there must be definite and indefinite integrals.

If there are only a finite number of discontinuities, then a definite integral exists; If there is a hop break, then the original function must not exist, i.e., the indefinite integral must not exist.

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sin^4x=[(1-cos2x)/2]^2=[1-2cos2x+cos^2(2x)]/4

1-2cos2x+(1+cos4x)/2]/4=(3-2cos+cos4x)/8

So. Talking about socks and socks sin 4(x)dx (3x-sin2x+sin4x haohuai4) 8+c

Calculation Answer] (4x+e)dx=2x+e+cCalculation method】Since the interferable problem function is composed of two basic functions, we can decompose it into two indefinite integrals.

4x+e )dx= 4xdx+ e dx] <>

Knowledge points of this question].

1. Integral addition and subtraction algorithm, <>

2. Basic integral Gong Nian Dan style, <>

3. For indefinite integral calculations, an integral constant c must be added

1 ((x Wu Jian Luyu 2) 2+1)dx

2∫1/((x/2)^2+1)d(x/2)2arctan(x/2)+c

If you don't understand, I wish you a happy study!

Summary. (4+x)/(4-x)dx

8-4+x)/(4-x)dx

8∫dx/(4-x)-∫dx

8ln|4-x|-x+c

4+x)/(4-x) dx

4+x)/(4-x)dx=∫(8-4+x)/(4-x)dx=8∫dx/(4-x)-∫dx=-8ln|4-x|-x+c

I would like to ask.

4+x)/(4-x) dx

3-4/dx

How did this solution come out?

4+x)/(4-x) dx

3-4/ x-4dx

How did this solution come out?

4+x)/(4-x) dx

3-4/ x-4dx

How did this solution come out?

Summary. Pro-<>

We will be happy to answer that according to the Newton-Leibniz formula, the calculation of the definite integral of many functions can be easily performed by finding the indefinite integral. Note here the relationship between the indefinite integral and the definite integral: the definite integral is a number, and the indefinite integral is an expression, and they simply have a mathematical computational relation.

A function can have indefinite integrals and no definite integrals, or it can have definite integrals without indefinite integrals.

Find x (4-x)dx

Dear <> glad to answer for you, are you sure that the original question is this, if the question is wrong, it may not be solved.

Dear <> will be happy to answer for you, and the detailed steps to solve this problem are as follows.

My dear <> will be happy to answer that according to the Bull Brigade Douton-Leflingbunitz formula, the calculation of the definite integrals of many functions can be easily carried out by finding the indefinite integrals. Here we should pay attention to the relationship between indefinite integrals and definite integrals: a definite integral is a number, and an indefinite integral is an expression, and they are only mathematically computational.

A function can have indefinite integrals and no definite integrals, or it can have definite integrals without indefinite integrals.