Which one of the following is an antiderivative of the function f(x)=sec²(2x+1) tan(x² + x + 1) tan(x + x) + 1 tan(2x + 1) + 1 1 -tan(2x + 1) + x 2 1 -tan(2x + 1) + 1

Q: Consider the function f (x) = x + cos x a) Find the x-value(s) (if any) for which f(x) has local…

A:

Q: tan (3r) dr = a tan(3x) – In(v1 + 9x²) +C 3 a tan (3x) + In(v1+9r²) 3. e tan '(3x) In(v1 - 9x² +C a…

A: We know that, from basic integral formula ∫tan-1x=xtan-1x-12log1+x2+C          ⋯⋯1 We have, the…

Q: Exercise 2: Let f(x) = sec2(x), and g(x) = tan2(x). Prove f'(x) = g' (x). Thus, find a C E R such…

A: Given,

Q: Evaluate the integral ftan¹ (x)sec (x) dx . O sec³(x) 5 O O tans (T) 5 O O None of these tan³ (x) 5…

A: find which method is use for integration.

Q: Solve y' = y'x.

A: solve y'=y2x3

Q: Find the local maximum, minimum and saddle points of the function using the second derivative test:…

A:

Q: Evaluate the integral [ 3 sec(x) tan(x)dx O 3sec(x) + C 3tan(x) + C O 3sec(x)tan(x) + C O None of…

A:

Q: (2x + 3)y' = y + √2x + 3, when x = -1, y = 0.

A:

Q: 23. Integrate: S x+2 dx 2 A. V1– x² + Sin-1x + C C. -V1– x² +Sin-1x + C B.V1 – x2 +Sin-1x + C D. –V1…

A:

Q: dx For - = In[F(x)]+C• What is f(/3) if C = 0? (x+x³) (x Tan-'x + 1) -1 - 6. + -1 - -15 -is -is

A: Integrate ∫dx(x+x3)(xtan-1x+1)

Q: Evaluate Stan" (x) sec¹x dx. 1 -tan (+2)(x) +-tan" (x) + C m+2 m 1 1 -tan (+1)(x) + -tan (™-1)(x) +…

A:

Q: Stan"( 1 -tan m+2 -tan m+1 m+1 1 m+3 Evaluate A B Ⓒ D tan" (x) sec¹x dx. (m + -2)(x) + ¹) (x) - 1)…

A:

Q: 3. ſsec? x(1+ tan x)/tan x – 1 dx ans : 3 (tan x – 1)' + ¿(tan x – 1) +c 4. S'cos x(2+ sin x)/2 +…

A: 3. Given integral is ∫sec2x(1+tanx)tanx-13dx Substitute tanx-1=z⇒tanx=z+1sec2xdx=dz Therefore, the…

Q: 1 /₁+422da dx 1+ 4x2 15. Evaluate (a) tan-¹(x) + C (d) tan-¹(2x) + C -1 (g) tan-¹(x) + C (j) None of…

A:

Q: Q.13.a) s dx x2+2x+1 b) Sx sinvx dx dx c) J Tx+V% 1E / E

A:

Q: 4) dependent Show that the following set of functions is Linearly independent or linearly f₂(x) = 3,…

A:

Q: Evaluate tan" (x) sec²x dx m 1 1 n (m + 2)(x) + tan -tan" (x) + C m+2 m 1 -tan (m + 1)(x) — . m+1…

A:

Q: Evaluate tan" (x) sec4x dx. 1 1 A -tan 2) (x). + (m+2 -tan" (x) + C m+2 m (m+1) ¹) (x) (m- m+1 1…

A: Evaluate: I=∫tanmxsec4xdx

Q: Let f be a differentiable function such that f f(x) sec² x dx = f(x) tan x-f3x² tan x dx . Which of…

A: Consider

Q: x² + 9 dx J x2 – 1)(x² + 4) | In \x + 1| + In |x – 1| +; tan-1 (-) + c -In |x + 1| - In |x – 1| -;…

A: Topic:- application of integration

Q: Let h(x) = tan(2x + 7). Then h' (3) is and h'' (3) is

A: Given query is to find indicated derivative

Q: . What is F(/3) if C = 0?

A:

Q: 1 -x2 + 6x dx = 10 - A In |-x2 + 6x - 10| + C -tan-1(x – 3) + C C -tan-1 (x + 3)+ C D tan-1(x – 3) +…

A:

Q: Let f(x) = -3cos x 2 tan x f'(2) = f' %3D

A: We can solve with the help of the differential

Q: z(r) = cos'(r)/1+r* ? cos (r) ( r Vi+r (1+r² 4 tan(r) cos'(-\/i + r*{ 4 cot(r) 1+r I tan(r) (1+r²

A: The given function is zr=cos4r1+r2.

Q: -tan (m + 1)(x) + C tan I + m um + ( x ) (x + ₁)² I m+3 1 с

A: Using substitution then integrating we get correct answer as (C)

Q: 1 Find that antiderivative of the function whose value at X = –1 is x2 + 4x + 5 0. x + 1 In |x+5 -…

A: