Use substitution to convert the integral to the integral of rational functions. Then use partial fractions to evaluate the integral. 2+e¯ O In (1 + 2e*) + C O In (1 + 2e*) + C Oin (2 +e) + C Oin (1 + 2e-*) +C

Q: Use the Table of Integrals to evaluate the integral. xdx S 2 x - 10x Select the correct answer. X -…

A: We have to find integration of given question.

Q: e+ dx Select one: O a. O b. O c. O d. O e. 4(x²-2x+2) · e¯X+C (x²-2x+2).ex + C (x²+2x+2).e¯X+C…

A:

Q: Evaluate the above integral using polynomial long division. Make sure to include "+C" in your…

A:

Q: 1. 5x+7 ܐ ] x3+ 2x – x =2 dx

A:

Q: Use the Substitution Formula to evaluate the integrals 7 0 √√y + 9 dy and dy and S √y +9dy. 0 -8

A: The given definite integrals ∫07y+9dy and ∫-80y+9dy. We have to find the value of the integral.

Q: 2. Use partial fraction decomposition to write the following rational expression as a sum of simpler…

A: Solution: The objective is to find the partial fractions

Q: Evaluate f 1 x-2x³/4-8√√T da by substitution of a = u and then partial fractions.

A:

Q: Evaluate the integral. 4x+10 x³+x 0_5 dx 4 x +C 10lnx +4tan-¹x+C O 10lnx+4tan-x-5ln(x²+1)+C…

A: GIven data

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.