Find the indefinite integrals (most general antiderivatives). You may need to try a solution and then adjust yourguess. Check your answers by differentiation. ∫(x3 + 5x - 7) dx

Q: Find the indefinite integral ∫ (e−3x + 2e2x + 3) / ex dx

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Q: 1. Г, 4x3 dx -2

A: We will find the value of the integral in the following step

Q: Use the Change of Variables Formula to evaluate the definite integral.

A: Use the Change of Variables Formula to evaluate the definite integral.

Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of…

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Q: Find the following integral. Note that you can check your answer by differentiation. 4x dx 2+ e4x

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Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of…

A: The objective is to find the given indefinite integral

Q: a) √ (³x²-²) dx S (3x2

A: In this question we have to find integration and after that We have to verify.

Q: Find the indefinite integral and check the result by differentiation.

A: To find the integral I=∫6x24x3-93dx

Q: Evaluate the definite integral.

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Q: find the most general antiderivative or indefiniteintegral. You may need to try a solution and then…

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Q: dy =

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Q: Find the indefinite integral and check the result by differentiation                   ∫x2(6 − x3)5…

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Q: Find the indefinite integral and check the result by differentiation

A: Given, I=∫x2-932xdx

Q: Find the indefinite integral and check the result by differentiation.

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Q: use the Change of Variables Formula to evaluate the definite integral.

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Q: Evaluate the definite integral. dx | 25 + (x + 4)2

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Q: How would I find the indefinite integral?

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Q: dx (x+5)+9

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Q: dx 15. x1+(In x)*]

A: Given:       ∫10dxx1+lnx2       =∫101x1+lnx2dx substitute u=ln x→dudx=1x→dx=xdu…

Q: Find the indefinite integral. ∫( (xe2x)/ (2x + 1)2) dx

A: Given Integral, ∫xe2x(2x+1)2dx We use the integration by parts rule to solve this integration.…

Q: Find the indefinite integral and check the result by differentiation.

A: Given, I=∫x34+1dx Or  I=∫x34+1dx

Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of…

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Q: use the Change of Variables Formula to evaluate the definite integral.

A: Given integral: Now,

Q: Find the indefinite integral ∫ 1/x√(9x2 − 49)   dx

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Q: Find the indefinite integral and check the result by differentiation.

A: Consider the provided integral, ∫2-3x10dx Find the indefinite integral and check the result by…

Q: Find the indefinite integral ∫ 1/ (x2 − 4x + 9)    dx

A: the given integral is: ∫1x2-4x+9 dx we have to find the value of the given integral. let the given…

Q: Find the indefinite integral.

A: Given:          ∫x2+2x-6x4dx Expand: x2+2x-6x4=1x2+2x3-6x4 Apply the sum rule: ∫fx±gxdx=∫fxdx±∫gxdx…

Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of…

A: We have to evaluate ∫  x32+8x+5dx. ∫ x32+8x+5dx=∫ x32dx+∫8x dx+∫5dx=x32+132+1+8·x1+11+1+5x +c, where…

Q: Find the indefinite integral below and check your work by differentiation: 1 S Væ + -dx

A: Solution: The objective is to find the value of given integral

Q: dx 15. x1+(In x)*]

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Q: Use one of the IBP formulas for definite integrals above (whichever you prefer!) to calculate xe dx.…

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Q: F( x) dx 2x sin

A: Definite Integration

Q: Find the indefinite integral ∫xe1−x2 dx

A: We need to evaluate the following integral: We will use u-substitution method u = 1-x2 du = -2xdx

Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of…

A: Apply the power rule of integration, ∫xndx=xn+1n+1+C So, the given integral is:…

Q: Find the indefinite integral. x + 7x2 + e) dx

A: The sum rule of integration states that ∫a+bdx=∫a dx+∫b dx. The constant rule of integration states…

Q: Find the indefinite integral and check the result by differentiation. Find 5. Enter the value of the…

A: Introduction: The antiderivative of a function is the indefinite integral, which is the opposing…

Q: Suppose we were instead asked to calculate the integral x sin(x) dx. Can you calculate this integral…

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Q: S-) dx 5.

A: Formula:∫ 1x dx = ln x+ C∫1a2+x2dx = 1atan-1(xa)+ C I=∫1x-5x2+1 dx=∫dxx - 5∫1x2+1dxI= ln x - 5…

Q: Find the indefinite integral and check the results by differentiation? (4x^2 + 3)^2

A: I=∫(4x2+3)2dx =∫(16x4+24x2+9)dxintegrateI=165x5+8x3+9x+c    where c is any constant

Q: e4x dx 6+ e4x

A: Given: I=∫e4x6+e4xdx

Q: Find the indefinite integral and check the result by differentiation                   ∫(x2 −…

A: Given, I=∫x2-932x dx

Q: Incardx (x)dx 4.

A: yes

Q: Find the indefinite integral and check the result by differentiation                     ∫x3(x4 +…

A: ∫x3x4+32 dx Put, x4+3=t⇒4x3+0=dtdx⇒4x3 dx=dt⇒x3 dx=dt4 Therefore, ∫x3x4+32 dx=∫t2 dt4=14∫t2…

Q: Find the indefinite integral. ∫(xe4x)dx

A: Given: ∫xe4xdx

Q: Evaluate the definite integral. dx 3x + 6 0.

A: This definite integral can be solved by using the Substitution method as explained in step 2.

Q: .4 2. Vx) dx

A: 2. We need to evaluate the following integral ∫141x2-xdx

Q: Find the indefinite integral. ∫(x2 + 2x − 6)/ x4 dx

A: Consider the integral: I=∫x2+2x-6x4dx……1

Q: Find the following integral. Note that you can check your answer by differentiation. dt 14

A: ∫ t+82t4 dtRewrite as : ∫ t2 + 16t + 64t4 dt⇒ ∫ 1t2 dt + ∫ 16t3 dt + ∫ 64t4 dtUsing formula : ∫ xn…

Q: (-5sin t) dt

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Q: Find the definite integral 10 (2х — 3) dx

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: