Q3) Evaluate the following integrals: sec(tan-1x). tan³ (tan-1 x) A) y = S dx 1+x2

Q: b. Stos-¹0 ¹(y) sinx √1+ sin2x dx dy

A: The given integral is, ∫01∫0cos-1ysinx1+sin2xdx dy. To find : Evaluate the integral. To evaluate the…

Q: r sin(T|2² - 1) cos² (7|2² - 11) da -3

A: To find the following definite integral.

Q: Integrate the following. - sec²x 3. ( sec?x tanx

A:

Q: Eval 7/3 (f) tan ³ 0 sec³ 0 d0 0.

A:

Q: x - 7 dx. /x². Evaluate the integral 2

A: Answer and explanation is given below..

Q: a) Find for 5x² – x³ sin y + 5e*y = 10 dx

A:

Q: Evaluate the integral 1 - √xé √x sec 1 2 sec | √xe¯ √x ³0c ² (2e √x - 2) dx = 2 ² (2e √x - 2) dx.

A:

Q: 1 dx J 2/3 (1+ x/3)

A:

Q: 1 Evaluate : dx. (1+x)Vx -x X-X

A:

Q: B1. Evaluate the integral | sinx (2 csc x- 4cot x) dx .

A: Given: The integral given is  ∫sinx2cscx-4cotxdx

Q: dr Find if r (x) = 9x 2 + 5x – 3. dx

A: Given,            r(x) = 9x2 + 5x - 3

Q: (ii) Evaluate the definite integral r³e² dr.

A:

Q: Let •T/24 I = tan°(4x) sec(4) dx. Express the value of • T/24 tan"(4x) sec(4x) dx 10 in terms of I.…

A:

Q: 1 dx Vx(1+ x)7

A: ∫1x1+x52dx

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: