5. Evaluate. . Evaluate. dx V7x dx = V7x + 2 . Evaluate. 2x2 xp- V1- 6x° S 2x2 dx%3D V1-6x3 Evaluate. SG 4x) (x* + 8x² +2)°dx SG- 4x) (x* + 8x² + 2) °dx = Evaluate. e dt Evaluate.

Q: sec4 dx

A: The integral is . Let . Differentiating both sides.

Q: b. S 2*³-4x²-x-3 dx х2-2х-3

A: First we divide the polynomial  using long division

Q: Which of the following functions is a solution of the exact equation? (6x + 4y)dx + 4xdy= 0.

A:

Q: Find y= Cot )

A: According to chain rule of differentiation ddxfgx=f'gx·g'x and according to division rule of…

Q: -| Vx³ + 16x² dx

A: Let I=∫x3+16x2 dx I=∫xx+16 dx Let assume x+16=t2⇒dx=2t dt I=∫(t2-16)t(2t) dt =2∫(t4-16t2)dt

Q: Vx+I dx. Vx +1

A:

Q: 2х -3 -dx. Evaluate(x-2)(x² + 1)

A:

Q: 4sinx+sinxsecx dx cos²xV4+secx

A:

Q: 3—4х dx =? Vx2+6x+1

A:

Q: 4-X 2-3X dydx

A:

Q: Evaluate 4x² + x3 2x² – 3x - 2 dx.

A: the given integral is (4x2+x-3)/(2x2-3x-2).

Q: Evaluate 3x? dx and , 3x² dx.

A: ∫02 3x2 dx=3x3302=x302=23-03=8-0=8

Q: 10. Evaluate (4x-8)ex²-4x+3 dx

A:

Q: Find domain and range of the * function y = Vx2 – 4x

A: To find the domain and range of  y=√(x²-4x)

Q: 3- f xvx2 +1 dx

A: Integration

Q: Rewrite (6x + 9) cos (x + 3x) dx using substitution of variables. o /3 cos udu o / 2 cos udu o / cos…

A: The given integral is: I=∫6x+9cosx2+3x dx

Q: fx x tan x dx

A: We can find the integration using integration by parts as below.

Q: 2x + 3 -dx. x2 + 3x + 4

A: To evaluate the integral: ∫2x+3x2+3x+4dx Evaluating the integral. Let substitute t=x2+3x+4…

Q: Find A if possible. If not, write “not defined". 1 8. A= 1 6 A- ) 3 1 9. А%3 9. 3

A:

Q: find dp/ dq. sin q + cos q = cos q

A:

Q: 1 2 3x + + 2x + 5

A: Given,         ∫13x2+2x+5dx

Q: Evaluate d (2 – 1) (z + 7)] | da O 3x^2 + 14x + 1 3x^2 14x + 1 O 3x^2 - 14x - 1 3x^2 + 14x - 1

A:

Q: 1- x 5. dx VI - r

A: