Solve the new Integral using the General Log Rule. Then, back-substitute x into the equation. (Remember to use absolute values where appropriate.) du - Injul + C x2 + 12x + 5 du dx = J+ 18x + 15x + 4

Q: 00 dx 3.

A:

Q: [eln ax - 2x log(x² + a)]dx 3.

A: Given: ∫eln ax-2xlogx2+adx To Find: Value of the given integration

Q: Solve the following integral: ∫x3(2 - x2)12    dx

A: Given: ∫x3(2-x2)12dx

Q: Evaluate the definite integral. e4 dx xylnx

A: We can evaluate the integral as below.

Q: (7x²) · e3*dx r1/2 cos(Tx) · ešin (r2)dx •ln(3) et Jin(2) ez +7dr et +7

A:

Q: Can you use the Log Rule to find the integral below? Explain. ∫ x / (x2 − 4)3 dx

A:

Q: /2 " sin'e cas Odo

A:

Q: Solve the following Integral Equation: Ho)-2.

A:

Q: (b) Solve the following integrals by using substitution and exponential rule and verify the answers.…

A:

Q: (x²+1)³ .dx

A:

Q: 5 (x² + 1)ž dx x8

A: I = ∫x2+152x8dxI = ?

Q: 2. - dx

A:

Q: 3 -1) da 1 x2

A: The given definite integral is: I=∫123x2-1dx=∫123x-2-1dx=3∫12x-2dx-∫121dx

Q: In the given equation , select the basic integration formula you can use to find the indefinite…

A:

Q: Define a substitution variable u and write ;dr in terms of only u. (2x – 1)2 You do not need to…

A: Given: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Can you use the log Rule to find the integral below? Explain. (x²-4)3 dx

A: Explained below

Q: Determine how large the number a has to be so that 1 dx

A: We have to find out the value of a .

Q: Recall that the constant term, C, cancels out when evaluating a definite integral and therefore, the…

A:

Q: Solve for the following integral: 1 -dx (e2x – 4)5/2

A: I=∫1(e2x-4)52  dxu=-2xdx=-12 duI=-12 ∫due-u-452v=e-u −4dv=-e-u du-dv(v+4)=duI=12∫1v52 (v+4) dv

Q: Which of the following integrals will NOT result into a natural logarithmic function? 5x xp: sec x2…

A: Evaluate each integral separately.

Q: Solve the integral: 3√x x² dx

A:

Q: √ √√x√1 - x-¹ dx

A: To find out the integration

Q: ne J反Inx dx

A:

Q: a) S In Gxt1) dx 2.

A: In this question we have to find the Integration. Formula Used, - Chain Rule. - ∫lnx=1x+C

Q: -3 x²+4x+3 dx 13.J, 33+2x2+x

A:

Q: -st cosht dt

A: We have to solve the definite integral                                                ∫0∞e-stcoshtdt

Q: What must be the value of C (constant of x² - 4 -dx so that the x +2 integration) to the integral of…

A:

Q: Solve the integral. x +1 -dx 4. 4 + x2

A: Our Aim is to integrate the expression given below:-∫x+1x2+4dx -(i)

Q: x2 dx V(12 – 8)5

A:

Q: Use the appropriate technique of integration to solve the following. (a) In x? + 1dx

A: SOLUTION-

Q: InX dx x7 8.

A: on solving integration by part method we get

Q: Find the definite integral of S: (2x – 1)' dæ 2 112

A:

Q: x² -25 dx 3x+15 e)

A: Given integration is : ∫x2-253x+15dx  To find the value of integration.

Q: 00 e-st cosh t dt

A:

Q: (log r) d.x 1+x²

A: The given integral is, ∫0∞logx41+x2dx

Q: Sx²e=* dx Sx²e¬

A:

Q: 2. S", sec t dt -T/4

A:

Q: Evaluate the integral: a log(1+x²)e- dæ

A:

Q: dx 1+ x6

A:

Q: e2 dx -2

A:

Q: Find the indefinite integral. (Note: Solve by the simplest method-not all require integration by par…

A: Integrate by parts

Q: Solve the integral: 1 √√√√√x+x dx

A:

Q: x3 dxp (x²+4)7

A:

Q: solve the given integration by substitution by sub

A: Given: ∫cos(lnx) dx

Q: T/° cos® 3 0de Co.

A:

Q: 2x2 + 2x + 11 dx (2x + 3)(x² + 4) (c)

A: Evaluating the integral using partial fractions.

Q: dx 나) | 10-10x

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 4 dx x2 ts

A: ∫13x4+1x2dx Formula ∫xndx = xn+1n+1+C

Q: T/2 sin & cas Ode sinte

A:

Q: 24 e121n(x²) 2)) dx

A: