Find the indefinite integral using any method ∫ (3x3 + 4x) /(x2 + 1)2 dx

Q: Use the Special Integration Formulas to find the indefinite integral. ∫ (√9 + 4x2)

A:

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 using any method.

A: The integral to be solved is . Substitute . Differentiate both sides.

Q: Find the following indefinite integrals through the substitution method. 10. (4- r)%

A:

Q: Evaluate the indefinite integral. (6x + 7 -dx x2 + 1

A: ∫6x+7x2+1dx

Q: Find the indefinite integral ∫(x3 − 4x2 − 4x + 20) / (x2 − 5) dx

A: Given ,∫x3-4x2-4x+20x2-5dx

Q: Evaluate the indefinite integral. In(x-6)dx

A:

Q: Calculate the indefinite integral:  ∫ (4x3 − 2x2)dx

A: Evaluate: ∫4x3-2x2 dx

Q: Evaluate the indefinite integral. 3x – 1 dx (3x² – 2x + 1)*

A: LetI=∫3x-13x2-2x+14dxPutu=3x2-2x+1then du=(6x-2)dxdu=2(3x-1)dxdu2=(3x-1)dx…

Q: 4 — бх4 - dx = + С. x2

A:

Q: Find the indefinite integral, Using Long Division Before Integrating                 ∫(x2 + x +…

A: Consider the given expression as

Q: Find the indefinite integral. x + 8x + 1 dx *+ 12x2 + 3x + 2

A: The given integral,∫x2+8x+1x3+12x2+3x+2dx

Q: Find the indefinite integral ∫ dx/√(1 − 4x2)

A: Consider the integral, ∫ dx/√(1 − 4x2) Let f(x) = 1/√(1-4x2) By using the trigonometric…

Q: Evaluate the indefinite integral. x + 4 dx x2 + 8x + 17

A:

Q: Find the indefinite integral ∫(x3 − 8x) / x2 dx

A:

Q: Evaluate the indefinite Integral 9x - dx 8x2 + 3

A: in the given integral  let  8x^2 + 3 =t           16xdx = dt            xdx = (1/16)dt         put…

Q: Find the indefinite integral ∫(2x2 + 7x − 3) / (x − 2) dx

A: Given integral is, ∫(2x2 + 7x − 3) / (x − 2) dx

Q: Find the indefinite integral ∫ (x2 − 2x) / (x3 − 3x2) dx

A: Given: ∫x2-2xx3-3x2dx for solving this integral we substitute  x3-3x2=t now differentiate both side…

Q: Evaluate the indefinite integral:  ∫ (x + 1)(x2 + 2x)3/4 dx

A: Given integral is ∫x+1x2+2x34dx. Consider u=x2+2x.

Q: Find the indefinite integral. x2 + 4x +3 dx x+ 6x2 + 9x +8

A: Given : Indefinite integral ∫x2 + 4x + 3x3 + 6x2 + 9x + 8dx   To find : Solution of given integral…

Q: Evaluate the indefinite integral. .3 6 + x*dx

A:

Q: Find the indefinite integral of (x2/(3+4x-4x2)3/2)dx

A: Consider the following integral: ∫x23+4x-4x232dx=∫x24-4x2-4x+132dx=∫x24-2x-1232dx Substitute…

Q: Find the indefinite integral by the method shown in Example 5. XVx + 3 dx

A: Given,          ∫xx+3dx

Q: Find the indefinite integral ∫ (x2 − 6x + 1)/(x2 + 1) dx

A:

Q: Find the indefinite integral. X< + 12x + 1 .3 dx to x° + 18x² + 3x + 4 ,2

A: Given: Let I=∫x2+12x+1x3+18x2+3x+4 dx To Find: To evaluate the given indefinite integral.

Q: Evaluate the indefinite integral. -dx 1 – x8

A: We use the standard integration result ∫11-x2dx=sin-1x+C

Q: Find the indefinite integral. 2 x+16x+2 x'+24x² +6x dx 2.

A:

Q: Find the indefinite integral ∫(4x3 + 3) / (x4 + 3x) dx

A:

Q: Find the indefinite integral ∫(x3 − 3x2 + 5) / (x − 3) dx

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find the indefinite integral ∫ 5/x√(9x2 − 11) dx

A: Given: ∫5x9x2-11dx

Q: Evaluate the indefinite integral of (x+3)/[(x-1)2(x2+2)] dx

A:

Q: Evaluate the indefinite integral

A: Given:

Q: Find the indefinite integral. dx | 7x2 +2

A: Given, I=∫x7x2+2dx

Q: Find the indefinite integral of (5/2x-3x/5)dx

A:

Q: Find the indefinite integral: Integral of (x3 - 3x divided by 3x2) dx

A:

Q: Determine the indefinite integral of ſ Vx6 + 3x5 + 3x4 + x³ dx

A:

Q: Find the general indefinite integral. x* + 4x +1

A:

Q: find the indefinite integrals (x^4+4x+8)/(x^2+2x+2)

A: Firstly, we take factors x^2+2x+2 common from numerator as shown on board.

Q: Find the indefinite integral using any method ∫cos x ln(sin x) dx

A: Given, ∫cos(x)ln(sin(x))dx

Q: Find the indefinite integral and check the result by 3/2 + 4x + 6) dx

A:

Q: Find the indefinite integral. x2 + 12x + 3 x + 18x2 + 9x + 6 dx

A: Integration is also known as antiderivative. Integtation of (1/x) = ln x

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

A: Given,            ∫x+3x2+6xdx

Q: calculate the indefinite integral.

A:

Q: 3x2ex3 dx

A: We have to find the given integral.

Q: Evaluate the indefinite integral: 3 3 x² dx + С. x3

A:

Q: Find the indefinite integral using any method ∫√(1 + √x) dx

A: Given: ∫ 1+x dxBy using the Substitution methods:Put   1+x =t…

Q: Find the indefinite integral ∫ (x2 + 4x) / (x3 + 6x2 + 5) dx

A: Consider the following integral: I=∫x2+4xx3+6x2+5dx Substitute x3+6x2+5=t→3x2+12xdx=dt→x2+4xdx=13dt…

Q: evaluate the indefinite integral.

A:

Q: x dx V3-2x-x

A:

Q: Find the indefinite integral of 3(x-1)(2-3x) dx

A: By using the simple rules of integral, we will solve the ∫(3(x-1)(2 -3x))dx integralNow,  ∫(3(x-1)(2…

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.