Employ the method of substitution to calculate J a(a* - 1)2 de = - 194 + K.

Q: Use a symbolic integration utility to find the indefinite integral. (Use C for the constant of…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) (7+5x)/(1+x2)  dx

A: Integrand, I = (7 + 5x) / (1 + x2) This can be split into two terms:  I = 7/(1 + x2) + 5x/(1 + x2)

Q: Identify u and dv for finding the integral using integration by parts. Do not integrate. ∫ (ln x)2…

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Q: Find the indefinite integral. (Use C for the constant of integration.) |zV 16z2 - 81 zp

A: ∫1x2+a2 dx = 1aarc tan(xa)+C

Q: evaluate the indefinite integral using techniques of integration ( integration by parts and…

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Q: Use the method of substitution to find the indefinite integral. Check your result by…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) secx tan x dx

A: ∫sec7x tanx dxu = sec7xdudx = 7 sec7x tanxdx = 17 sec7x tanx du⇒17∫1 du= u7substituting u = sec2x=…

Q: Calculate the indefinite integral x²sin(x)dx Show your calculations.

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Q: Find the indefinite integral. (Use C for the constant of integration.) dz zV 25z2 - 49

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Q: Use integration by parts to evaluate the definite integral: 0.9 -200 dx 5xe %3D -0.8

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Q: Use IBP to evaluate the indefinite integrals. 1. ∫ x³sin x dx 2. ∫ sec³ x dx 3. ∫ x cot² x dx

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Q: / (22* + 3,/5 +) Calculate the indefinite integral: dz

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Q: Find the indefinite integral. (Use C for the constant of integration.) 9. dx xV 81 - (In x)2

A: Given integral  ∫9x81-lnx2 dx keep in mind the formula  ∫dxa2-x2 =  sin-1xa+C

Q: Evaluate the integral using integration by parts where possible. (Use C for the constant of…

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Q: Use an appropriate u-substitution to evaluate the indefinite integral -dt. Use C'for the constant of…

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Q: Find the general indefinite integral. (Use C for the constant of integration.) 8. x° dx

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Q: Use substitution to find the indefinite integral. 2 | 5z² – 3 dz -3 dz =

A: Given: I=∫z5z2-3dz   ...1   As we know the Power rule: ∫xndx=xn+1n+1+C

Q: Find the indefinite integral. (Use C for the constant of integration.) 9. dx XV 81 - (In x)2 |

A: Here we will solve the given integral,

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) X³VX2 + 19 dx

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Q: Evaluate the indefinite integral. (use C for the constant of integration.) dx = 6(8 + gx) %3D

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Q: Improper Integral. Explain why 4. .1 dx +0 ,3 -1 * -

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Q: Find the Indefinite Integral and check the result by differentlation. dx (5x)- Step 1 To obtain the…

A: topic - indefinite integral

Q: intergral 5 tan^4x dx Integrate/find the indefinite integral

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Q: Find the indefinite integral. Check your result by differentiating. (Use C for the constant of…

A: Given that: ∫(2x3-12x)3(x2-2)dx

Q: Evaluate the integral by u-substitution. (Use C for the constant of integration.) Integral of…

A: Given : Integral ∫Sin3(x) cos(x) dx   To find : Evaluate the integral by u-substitution?

Q: Evaluate the integral using integration by parts where possible. (Use C for the constant of…

A: ∫(x2-4)e2xdx

Q: Match the integrals in the left column with the correct evaluation method in the right column. Using…

A: We have to match the left  column with the right column.

Q: Integral of sinh(e^lnarccot3x)dx/(1+9x^2)

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Q: Calculate the integral. (Use C for the constant of integration.)   dx x   4x4 − 1

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Q: Find the indefinite integral. Check your result by differentiating. (Use C for the constant of…

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Q: Determine the value of the integral: integral sign:  (x^2)(e^-x^3)

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Q: Find the Indefinite Integral and 5x + dx (5x), Step 1 To obtain the glven Integral, rewrite the…

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Q: Please help me solve the attached problem

A: Solve the indefinite integral as follows.

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) /(6 - 5x)8 dx

A: Given:

Q: Use integration by substitution and the Fundamental Theorem to evaluate the definite integral. 2 |…

A: Use substitution method

Q: Find the indefinite integral. Check your result by differentiating. (Use C for the constant of…

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Q: Use the method of substitution to find the indefinite integral. Check your result by…

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Q: Identify u and dv for finding the integral using integration by parts. (Do not evaluate the…

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Q: | rv25 – x2 Evaluate the indefinite integral. dx xv 25 – x2 -

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Q: Evaluate the integral using integration by parts where possible. (Use C for the constant of…

A: *to find:- integral value of the given function.

Q: Use the general power rule for integration to find the indefinite integral. a)∫10x/(√5x2+13) dx…

A: a) The general power rule of integration is of the form ∫fxnf'xdx=fxn+1n+1+c   Let fx=5x2+13. So…

Q: Identify u and dv for finding the integral using integration by parts. Do not integrate.      ∫xe9x…

A: Given: ∫xe9x dx To determine: Identify u & v for finding the integral using integration by…

Q: 2 dax (x³-5)3 5)3

A: Please refer the attached image for complete solution.

Q: x2 dx (4x³ + 7)²

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) | sec2(0) tan²(0) de

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Q: Use integration by parts to evaluate the integral. (Use C for the constant of integration.) In(4x)…

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Q: Find the Indefinte Integral and check the result by differentiation. 5x + (5x) Step 1 To obtaln the…

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Q: Indefinite integral of   ∫y+3/(3-2)^2/3dy

A: The given Indefinite integral is ∫y+33-223 dy. Evaluate the above integral as follows.

Q: Integrate using trigonometric substitution Integral of x/(x^2-1)dx

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Q: Evaluate the indefinite integral. (Use C for the constant of integration. | (5 - 4x)10 dx

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.