Question

give me some formulas of integration​

Answer 1

Answer:

sin x dx = -cos x +d is the right answer

Answer 2

Answer:

Explanation:

The notation, which we're stuck with for historical reasons, is as peculiar as the notation for derivatives: the integral of a function f(x) with respect to x is written as

∫f(x)dx

The remark that integration is (almost) an inverse to the operation of differentiation means that if

ddxf(x)=g(x)

then

∫g(x)dx=f(x)+C

The extra C, called the constant of integration, is really necessary, since after all differentiation kills off constants, which is why integration and differentiation are not exactly inverse operations of each other.

Since integration is almost the inverse operation of differentiation, recollection of formulas and processes for differentiation already tells the most important formulas for integration:

∫xndx∫exdx∫1xdx∫sinxdx∫cosxdx∫sec2xdx∫11+x2dx=1n+1xn+1+C=ex+C=lnx+C=−cosx+C=sinx+C=tanx+C=arctanx+C unless n=−1  

And since the derivative of a sum is the sum of the derivatives, the integral of a sum is the sum of the integrals:

∫f(x)+g(x)dx=∫f(x)dx+∫g(x)dx

And, likewise, constants ‘go through’ the integral sign:

∫c⋅f(x)dx=c⋅∫f(x)dx

For example, it is easy to integrate polynomials, even including terms like x√ and more general power functions. The only thing to watch out for is terms x−1=1x, since these integrate to lnx instead of a power of x. So

∫4x5−3x+11−17x√+3xdx=4x66−3x22+11x−17x3/23/2+3lnx+C

Notice that we need to include just one ‘constant of integration’.

Other basic formulas obtained by reversing differentiation formulas:

∫axdx∫logaxdx∫11−x2−−−−−√dx∫1xx2−1−−−−−√dx=axlna+C=1lna⋅1x+C=arcsinx+C= arcsecx+C

ssorry for this lang