If necessary, use two or more substitutions to find the following integral. dx (Hint: Begin withu= /6+x.) 17+ v6+x

Q: Evaluate VSinx dox Vsínx+VCosx

A:

Q: Evaluate: x – 2 dr

A:

Q: 8. Evaluate S dx x4+x² + 1

A: To find:- ∫0∞dxx4+x2+1dx

Q: 6 后 X-T dx

A:

Q: Evaluate∫cos 6x dx without using the substitution method.

A:

Q: Evaluate the function shown

A:

Q: 6. dx (x2 + 2x + 2)²

A:

Q: Evaluate |승 cosec22x dx

A: We have to find the indefinite integral

Q: Væ2 - 64 dx. Evaluate

A: To evaluate: I=∫x2-64x3dx Substitute u=x2-64⇒du=12x2-64(2x) dx⇒dx=ux du

Q: 16 dx 11. Vx-1 9.

A:

Q: Evaluate dx 2 1-x

A: We have to evaluate ∫23x1-xdx. We know that ∫dxx2-a2 = 12aln x-ax+a+C

Q: S Vx2 – 8x + 25 dx

A:

Q: L Vx + 12x2 + 5 tanx dx

A:

Q: Integrate x² √6 +25 1 dx + C

A:

Q: Evaluate x²7² dx

A: We will use u.v rule of integration.

Q: cV9-x² ¢V9¬x² dz dy dx

A: Explanation of the answer is as follows

Q: 1 Evaluate : dx x'x-1 .3

A:

Q: 6. Evaluate the following integrals. 1/4 (2) [¹ sec³ πt dt

A: 6. ∫014sec3πt dt Note:    Multiple questions are given, we are answer with only one question.

Q: find dy/dn in5 フx 34+2

A: Since you have posted multiple question We solve only first question  for reaming question post…

Q: I. Evaluate S x² +6 x³ + 3x dx.

A:

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.