Find the value of the following definite integrals. Show your solution. 1. L* + 4) dx 2. f(cos x + tan x) dx 3. x? + 2x +1)dx

Q: x³ dx 9+x* 1.

A:

Q: dy Q10., Solve (1+ x²) + y = tan¬1x. dx

A:

Q: 2x-1 dx

A: Given,

Q: Find [(x- sin(2x)) dx

A:

Q: S sin 2x sin 4x dx 7.

A:

Q: 5. Change of variable 2 x dx 3x+1 a.

A: Given function, ∫12x3x+1dx

Q: 5. Solve for x² − x+6 x³ + 3x 1³ dx.

A:

Q: (2x³-9x²+2) dx from x = 6 to x = 11

A: Given: ∫2x3-9x2+2dx   from x=6 to x=11

Q: Find √√3 x² +3 x² +1 dx

A:

Q: Sx sech2 x² dx

A: Given:  Integral of xsech2x2

Q: 3. Evaluate f x sin2 (x²) dx.

A: Given I=∫x sin2x2 dx To Find I

Q: 3. tan x dx

A: Formula: tan2x=sec2x-1

Q: -dx x +1 2 5.

A:

Q: S(6x + 2) sin(6a² + 4.x)dx

A: we have to integrate

Q: Evaluate Set 7x cos (6x) dx. Sex cos (6x) dx =

A:

Q: 312 dx x + 1

A: We have to find the value of ∫x3/2x+1dx

Q: 1. Solve. X x²-5 +5r+0 - dx

A:

Q: Integrate the given function. T/ 20 2 sec 5x -dp- 4 + tan5x 1/20 2 sec 5x 1 5 -In 4 - 4 + tan5x | LO

A: The given integration is:

Q: 3 dx 4+x2 00 Find

A: Let I=∫2∞34+x2dx. Simplify the integration I by using the constant multiple rule.…

Q: 2. f (√x - 72 dx

A: