x+3 dx x²+6x+7

Q: dx а. 3 x²(9x² – 4) .2 -

A: The integration of the integral is 1/[x2(9x2-4)3/2].

Q: 2x Use substitution to evaluate the integral dx (x² + 3)°

A: We have to apply rules of integration to solve the problem Power rule: xn =( 1/n+1)(x)n-1

Q: Evaluate the integral. Vx² +9 dx

A: In the given question first use the substitution method and then use the properties of indefinite…

Q: Evaluate the integral x3 + 39 dx. + 4x + 3 x2

A: Try to simplify the numerator in terms of the denominator.

Q: Evaluate the integral. dx 7x(1 + 7x)

A:

Q: Evaluate the integral. 2 dx x2 + 4x + 20

A:

Q: use trig substitution for integral of [(x^2-1)^1/2]/x^4

A: To integrate the given rational function,using the appropriate trigonometric transformation

Q: Evaluate the integral (2x + 6)dx x² – 2x + 17

A:

Q: 3x8 dx V2 – x3 2 —

A:

Q: Find the integral

A: To evaluate the integral: ∫x25-9x2dx Solution: ∫x25-9x2dx…

Q: Evaluate the integrals: 2x³-2x2+1 dx x3-x2

A: I = ∫2x3-2x2+1x3-x2 dx

Q: Use any method to evaluate the integral. dx X>11 (x²-121) 3/2

A:

Q: Evaluate the integral. | (7x2-6x +7) dx

A:

Q: Evaluate the integral. 0.6 x2 dx V 9 - 25x2

A:

Q: Evaluate the integral. dx 3x2 + 11x + 6 0.

A:

Q: Use the tabular method to find the integral. x²(x – 2)/2 dx

A: Use tabular method to find the integral  ∫x^2(x-2)12dx sign Derivative Antiderivative + x2…

Q: x + 2 x3 - 2x² - 3x dx

A:

Q: Evaluate the integral. •2 /2x² – 4 dx = 7x

A:

Q: 9x2 - 4 dx

A: Given that, Apply u-substitution: Differentiate both sides with respect to x, Plug the values of…

Q: dx x4+16x²

A:

Q: Evaluate the integral. х3 — 5х — 8 dx x2 — х — 6 -

A:

Q: 1 dx x² Vx2 – 9 3.

A: Given ∫3∞1x2x2-9 dx We have evaluate the integral. Formul;a will use1.∫sinxdx=cosx2. sec2x-1=tan2x

Q: Evaluate the integral. (6x2 - 8x + 4) dx

A: Given integral is definite integral. So we first evaluate it and then we will put limit. PFA here…

Q: Evaluate the integral. dx x2 + 4x + 20

A: Solution: ∫02xx2+4x+20dx

Q: dx 5x2 + 16

A:

Q: dx ,2 /9 – x² 2

A: Solution

Q: Evaluate the integral. r5 x3 – 3x² – 9 dx J4 x3 – 3x²

A:

Q: Find the integral 13x³ + 6x² + 7x + 2 dx= (x + 1)²(x² + 1)

A:

Q: Find the integral (4x2 – 21x) dx (x – 3) (2x + 3)

A: The partial fraction decomposition or partial fraction expansion of a rational fraction is an…

Q: Evaluate the integral 9x² √x² + y² dzdy dx

A: Given problem:-

Q: evaluate the integral.

A: Given integral:

Q: Find the integral ∫ dx / x2−5x+7.

A:

Q: x(4+ x²)!/3 dx

A:

Q: Evaluate the integrals using the substitution method of 3x2(x3-4)9 dx

A: Given: Let I=∫3x2x3-49 dx To Find: To evaluate the given integration using the substitution method.

Q: Evaluate the integral ∫2x+3 / x2−9 / dx.

A: Now consider,

Q: Evaluate the integral. (2x2 dx +X +

A:

Q: Evaluate the integral: X³VX2 + 4 dx =

A:

Q: Evaluate the integral. 9x2 +x +1 -dx

A: Solve by integration

Q: Find the integral ∫(x3 + x)5(3x2 + 1) dx.

A: we have to find the integral of ∫(x3 + x)5(3x2 + 1) dx.

Q: 3 x° +x* dx x² 4 3

A: The given integral is solved below in detail.

Q: Evaluate the integral. 2x /x² + 9 dx

A:

Q: Evaluate the integral. 2. (9x2 - 8x + 6) dx

A: the Integration is a process of finding the anti derivative of a function. There are basically two…

Q: Evaluate the integral x°Vx² + +9 dx. 2 +9 dx =

A: The given integral is, I=∫x3x2+9dx lets substitute, x2+9=z2⇒x2+9=z⇒xdx=zdz Substituting the above…

Q: Evaluate the integral (9x2 +4x +2) dx

A:

Q: Evaluate the integral. 8. dx (x² – 1)3/2

A:

Q: Evaluate the integral. [² (7x)√x² + 34√x³ √√√x dx

A:

Q: Evaluate the integral dx (7x + 6)2

A:

Q: Evaluate the integral ∫dx / x2+4x+8.

A:

Q: Evaluate the integral ex dx 2x 3e2x 2e

A: Given integral, ∫ex2e-2x-3e2xdx.   It is integrated as follows: Apply u-substitution, u=e-2x.…

Q: Evaluate the integrals using the trig substitution x dx 2. Vx² + 1

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.