Finding integral ∫ (x ^ 3 + e ^ 3x + cos3x) DX

Finding integral ∫ (x ^ 3 + e ^ 3x + cos3x) DX

∫(x^3+e^3x+cos3x)dx
=∫x^3dx+∫e^3xdx+∫cos3xdx
=(x^4)/4+(e^3x)/3+(sin3x)/3+C

Finding indefinite integral 1 / (1 + cosx) DX ((xcosx + SiNx) / (xsinx) ^ 2) DX (x ^ 2 + 1 / (x ^ 3 + 3x + 1) ^ 5) DX 4arctanx-x / (1 + x ^ 2) DX

This is a senior high school problem. Step by step, first you can simplify 1 / (1 + cosx) / SiNx, and then you can find an example to do it yourself

∫(3x^2+1-e^x)dx

=x^3+x-e^x+C

∫1/(x^100+x)dx ∫1/(e^x+e^3x)dx

1. ∫ 1 / (x ^ 100 + x) DX = ∫ 1 / X - x ^ 98 / (x ^ 99 + 1) DX = ∫ 1 / X DX - ∫ x ^ 98 / (x ^ 99 + 1) DX = LNX - 1 / 99 * ∫ 1 / (x ^ 99 + 1) d (x ^ 99) = LNX - 1 / 99 * ln | x ^ 99 + 1 | + C C is constant 2, ∫ 1 / (e ^ x + e ^ 3x) DX = ∫ 1 / [e ^ x * (e ^ 2x + 1)] DX = ∫ 1 / e ^ X - e ^ X /

() articles () music words

Writing listening

The positions of line segments AB and Cd in the plane rectangular coordinate system are shown in the figure. O is the coordinate origin. If the coordinates of a point P on line segment AB are (a, b), then the coordinates of the intersection of line OP and line segment CD are (a, b)______ ．

Let the intersection of line OP and line segment CD be e, ∵ ab ∥ CD, and O, B and D are on the same line, OB = BD ∥ OP = PE ∥ if the coordinates of point P are (a, b), ∥ the coordinates of point e are (2a, 2b). So the answer is (2a, 2b)

The surface area of a cuboid is 208 square centimeters, the bottom surface is 8 centimeters long and 6 centimeters wide?

Let the height of the cuboid be X
Then 8x * 2 + 6x * 2 + 6 * 8 * 2 = 208
The solution is x = 4
So the cuboid volume is 6 * 8 * 4 = 192

Expand sin (PAI / 4-x) to get √ 2 / 2 × (SiNx cosx). How do you get this?

sin(π/4-x)=sinπ/4cosx-cosπ/4sinx=√2/2cosx-√2/2sinx=√2/2(cosx-sinx)

Let I1 + I (where I is an imaginary unit) be a root of the real coefficient equation 2x2 MX + n = 0, and find the value of | m + Ni |

x1＝i1+i＝1+i2，… (2) x2 = 1 − I2 So 1 + I2 + 1 − I2 = m2, M = 2 (6 points) 1 + I2 · 1 − I2 = N2, n = 1 Therefore, | m + Ni | = | 2 + I | = 5 (12 points)

Monotone interval of functions y = x + 2 / X and y = x / x square + 9
Senior three mathematics Today's homework I can't do it

Y = (x + 2) / X is reduced to y = 1 + 2 / X
(- infinity, 0) simple minus (0, + infinity) simple increasing
Is y = x / (x ^ 2 + 9) wrong?
To provide you with a method, I don't know if you have learned it
Derivative of y = (9-x ^ 2) / (x ^ 2 + 9) ^ 2
So (- infinity, - 3) single minus (- 3,3) single plus (3, + infinity) single minus