Finding the indefinite integral of e to the xth power sin xdx? 200

Correct, the last step and one more transformation will give you the standard answer.

<>That's right, simplifying it is the same as the answer.

That's right, just keep it simple. Share another solution. sin x=(1-cos2x) 2, original = (1 2)e x-(1 2) (e x)cos2xdx.

Let a= (e x)cos2xdx and b= (e x)sin2xdx. Applying Euler's formula, a+ib= e [(1+2i)x]=[1 (1+2i)]e (x+2ix)+c.

Whereas, 1 (1+2i) = (1-2i) 5, e (x+2ix) = (cos2x+isin2x)e x. ∴a+bi=(1/5)[(cos2x+2sin2x)+i(sin2x-2cos2x)]e^x+c。

Original = (1 2)e x-(1 2)a=(1 10)(5-cos2x-2sin2x)e x+c.

Using the partial integration method, the specific solution process is as follows: e x·sin2xdx

e^x·sin2x-2∫e^xcos2xdx

e^x·sin2x-2[e^x·cos2x+2∫e^x·sin2x]dx

e^x·sin2x-2e^x·cos2x-4∫e^x·sin2x dx

5 e x·sin2xdx = e x·sin2x-2e x·cos2x+c1

Therefore e x·sin2xdx=1 5·e x· (sin2x-2cos2x)+c。

When solving the indefinite integral, we do not find the range of the tiny spatial variable dx, but it should change on the curve to the power of x.

Ask for the points that are not set by God:

1)。∫e^(-x)dx

Solution: Original formula =- d[e (-x)]=e (-x)+c2). ∫sinx∣dx

Solution: When 2k x (2k+1) talks about the hood, sinx 0, then sinx loses dx= sinxdx=-cosx+c;

When (2k+1) x 2(k 1), sinx 0, sinx dx=- sinxdx=cosx+c;

The integral constant c that follows, which is written as 4k or 4k+2 in your answer, may have its special needs to solve the problem, and it doesn't matter.

xe^x dx

x d(e^x)

Partial Dispersion Integral Method:

xe^x - e^x dx

xe^x-e^x+c

x-1)e^x+c

If you don't understand it, please ask, 1, Yoyo Valley Yusui Report the area of the figure enclosed by the parabola y=x*2 and the straight line y=1 Thank you s= (1,1) 1-x 2 dx

x-x^3/3 | 1,1)

4/3,

Summary. Hello dear customers, there are three questions in one round of middle and high school mathematics and two questions in one round of advanced mathematics, thank you for your understanding!

Calculate indefinite integrals (x+e'-sin+x)dx.

Hello dear customers, there are three questions in one round of middle and high school mathematics and two questions in one round of advanced mathematics, thank you for your understanding!

You're this e'What is it.

That's it.

You send a picture and I'll take a look.

It's not logical.

Pictures cannot be posted. How can there be an e'

It's ex you ha.

Find the monotonic interval and extrema of the function f(x)=x3-3x2-9x+14.

x3 3 is on top of x. 3x2 2 is on top of x.

I know. Wait.