-T/4 sin x 1+cos²x

Q: eSz sin(6x)dx —

A: For the  I=∫eaxsin(bx) dx =eaxa2+b2asin(bx)-bcos(bx)+C (Using integration by parts)

Q: 1 x² + 6x + 12

A: Integrate: ∫1x2+6x+12dx

Q: 4x V1- x³ dx

A: We will evaluate the given integral.

Q: sec2 3x dx J tan²3x-3 tan3x+2

A:

Q: Find the integral.

A: Given,

Q: Evaluate the following integral: JIS [xlnytan z dV if S = {(x, y, z) € R³ : − 1 ≤ x ≤ 0, e ≤ y ≤ 2e,…

A:

Q: 2. [f 5y ey dA, F- {(x, y): 0 s x s y?, 0 s ys 2} F

A:

Q: et + dx

A:

Q: | sin 3x sin 6x dx

A: Given: ∫sin3xsin6xdx

Q: q. r. √y² - 25 -dy, y > 5 y³ dx x²√√x²-1 2 ,x > 1

A: Solve both integral as following:-

Q: 2 E2 72-00 (i = 1 Express lim + Si ⅱ) (2) as a definate integral.

A:

Q: 4. cscó 3x dx 5. ſ cots x dx

A:

Q: Find the integral:

A: Recall the formula:

Q: Explain and Find the integral of the ff : dx 4 dx 2) 1 3) dx =

A: We have to find the integral: 1.  ∫1+5x2xdx2.  ∫x-54dxx3.  ∫14+7e-xdx This will be solved by…

Q: 4x²+3x+2 dx x²(x+1)

A: To integrate the given function.

Q: (1) / : dr. x² + 4

A: For the first sub part we use the standard formulas for integration.