Let  un = x4 + 7x2.  Find  du dx

Q: If Arctan gx 3. dx =b Arctan* 3x +C, what is b?

A: Solving the given integral by substitution.

Q: If 3y-5x = 7, then at (-1,2) is dx %3D

A: This problem can be solved by differentiating the given implicit equation w. r. t x and then finding…

Q: Find the derivative. d. (In (9x? + 4)) dx di (In (9x? + 4)) =| dx

A: Solution:To find:ddx ln (9x2+4)=?Formula:ddx(log x)=1xddx(xn)=nxn-1

Q: Find dy dx 5x 11 100

A: The given function is: y=5x8   As we know that; The Power law; ddxxn=nxn-1 And a·f'=a·f'

Q: Which of the following is equal to (2° – 7æ)*dx = (x6 -

A:

Q: |(9 – x²) dx

A:

Q: fx' tan" (e* ) dx 6.

A: Solve by substitution method

Q: following x² dx

A:

Q: 2x fe²x sinx dx

A: Using integration by part.

Q: Find and simplify whenever possible. dx y =cosh3 2x – cosh 2x - 3

A: Given y=13cosh3(2x)-cosh2x We need to find the value of dydx dydx= ddx13cosh32x-cosh2x =…

Q: fx' sin 3x dx

A: Given, ∫x2sin3xdx  We have to find the integral.

Q: e tan (e") dx Vsec2 (eª) – 7

A: Use substitutions method for finding the integral.

Q: d -(In(5x + 4)) dx Find

A:

Q: Evaluate. (Be sure to check by differentiating!) 6. dx, x4 5. 一 6+5x

A:

Q: Find (d/dx) (sqrt(x)/cos(x))

A: Firstly, we use quotient rule of differentiation  and , we use the power rule of differentiation to…

Q: Evaluate. (Be sure to check by differentiating!) | 16. dx

A:

Q: S,(3x2 – 2x + 1) dx

A: We know the integral formula, ∫xndx=xn+1n+1+C

Q: [s sec5 x tan4x dx

A:

Q: sec? 5x dx

A: Given query is to find the integral .

Q: So (2+7x) et ¹ dx

A:

Q: Find fre dz |2e*dx

A:

Q: S,(3x + a)dx = 10 , then a =

A: Given: ∫123x2+adx=10 As we know that; The Power rule: ∫xndx=xn+1n+1+C ; n≠-1 And ∫a·fxdx=a·∫fxdx;…

Q: Evaluate. (Be sure to check by differentiating!) 9 dx, x+ - 9+4x

A: ∫1xdx=ln(x)+C

Q: Use an appropriate substitution to integrate Jaco 24xcos (x²-2) dx

A:

Q: 5 ex dx e2x

A: Given: ∫5-exe2xdx

Q: dy Find if dx (² + 7)* 3 5,

A:

Q: Find the values of a that make: ja- |(x– 2)dx = 6

A: Answer

Q: Find, (x²e*dx

A: use integration by parts take the rule is

Q: S tan° 4x seco 4x dx а.

A:

Q: Evaluate A) Scos³x dx 4 B) Ssecx tanx dx

A:

Q: S sin*3xcos*3xdx

A:

Q: dx

A:

Q: Evaluate: 2 (+8xy) dy dx

A:

Q: Show that for B > 0, Be-Ba dx = 1. |

A:

Q: If y = cos(5x³), find and y dx2 dx

A: Given that  y = cos(5x3) we need to find y' and y". Where y' = dy/dx and y" = d2y/dx2 Now, y =…

Q: If (4f(x)+7) dx = 15, then L f(1)dx =

A:

Q: So xV1 – x2 dx (use substitution method)

A:

Q: Kindly sotve por : Dx (In | v | ) = Dx ((tan (3x) - In | 2x| + ( x³ - In | e|) - In | Inx | )

A: On differentiating Lhs: ddx(ln y)=1y.dydx on differentiating Rhs: ddx( tan(3x).ln|2x| +…

Q: S tan³x sec³x dx

A:

Q: fx cos 2x dx

A: Let's solve given integration.

Q: Evaluate. (Be sure to check by differentiatingl) 1 dx, x# - 3 9+ 3x

A: To evaluate: I=∫19+3xdx Use the rule: ∫1xdx=ln |x|+C

Q: 7. Sxtan-x dx

A: Given: The integral is  ∫xtan-1x dx     Formula used: Integration by parts: ∫udv=uv-∫vdu

Q: 3 Given that ex dx = e³ – e, use this result to evaluate 7ex + 4 dx.

A:

Q: Vsin² 2x dx =?

A: Given ∫02πsin2 (2x) dx Remember sin2 (2x) is always positive. Thus, sin2 (2x) should be positive for…

Q: 3. to 4. Hox - 9x²+8dx 2- 十一X dx

A: ∫10x4-9x2+8x2dx

Q: Je sin( -4x)dx 3r Su

A:

Q: +7) dy dx 4x+

A: Evaluate the given integral as follows. ∫02∫x22x4x+7 dy dx=∫02∫x22x4x+7 dy dx=∫024xy+7yx22x…

Q: Evaluate the integral.

A: We have the given integral as I=∫012x+3x+12dx On solving further, we get the result as…