Find the indefinite integral ∫ (x2 + 2x + 3) / (x3 + 3x2 + 9x)   dx

Q: Find the indefinite integral.

A: We find this indefinite integral by the method of substitution. We re-write the integral in a…

Q: Find the indefinite integral 3. |(6x² + 4x – 9)dx

A: Given, The indefinite integral  ∫6x2+4x-9dx  We have to evaluate it.

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

A: Evaluate: ∫4x3-2x2 dx

Q: Find the indefinite integral ∫(5 + 4x2)2 dx

A:

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

A: We have to evaluate

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. 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: L( -x² + 2x² – 1)dx

A: To give the corresponding indefinite integral. To show the complete solution. ∫-22x5-x3+2x2-1 dx

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

A:

Q: Find the indefinite integral ∫(x3 − 6x − 20) / (x + 5) dx

A: Given: ∫x3-6x-20x+5dx for integrating this we substitute x+5=u now differentiating both side with…

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: Consider the indefinite integral (4x³ + 5x² − 1x − 6 [420³ + x² - 1 dx

A:

Q: Find the indefinite integral ∫ 1( 4 + 4x2 + x4)dx

A:

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 x3 + 6x2 + 9x + 8

A:

Q: find the indefinite integral of (3lnx)/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.

A: Given integral: ∫x2-2xx3-3x2dx

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

A:

Q: Find the indefinite integral. 16x(8x² + 6)* dx + 6)

A:

Q: Find the Indefinite Integral. dx 12-3x

A:

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. 5x2 dx et

A:

Q: Find the indefinite integral.

A: Consider the given integral as ∫x+13x2+6xdx

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 ∫xsinx2 dx

A: Given: The integral ∫xsinx2dx, To evaluate: The given indefinite integral.

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

A:

Q: Find the integral [(3x² – x) In(3x)dx .

A: Given query is to solve the integral.

Q: Find the indefinite integral. x² + 4x + 3 dx x3 + 6x2 + 9x + 8

A:

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

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: Evaluate the indefinite integral x5 - 5x dx x3

A: This is a simple question related to integration  Solution is given below

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

A:

Q: Find the indefinite integral. ∫(x2 + 2x − 6)/ x4 dx

A: Consider the integral: I=∫x2+2x-6x4dx……1

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: evaluate the indefinite integral.

A: To solve the indefinite integral.

Q: Find the indefinite integral. x² + 4x + 5 dx x3 + 6x² + 15x + 8

A:

Q: Evaluate the indefinite integral x5 – 5x dx x3

A:

Q: x dx V3-2x-x

A:

Q: Evaluate the indefinite integral: x(7+6x³) dx +C.

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…