Evaluate the following definite integral. Show all intermediate steps. ∫12   [ 2xe^(x^2+1) + (9x^2+12x+3)/(x^3+2x^2+x)^3/2]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 by making a change of variables

A: Given integral is By using the following substitution , we get

Q: Find the indefinite integral. (Use C for the constant of integration.) 4x(2x² + 3)6

A: Here we have to find the indefinite integral.

Q: Find the indefinite integral by making a change of variables.

A:

Q: Evaluate integral of dx/x-2 from -6to-10

A:

Q: Find the indefinite integral by making a change of variables. (Use C for the constant of…

A: Obtain the indefinite integral of the given  by substitution method.Let the variable  be x + 6.

Q: Evaluate the indefinite integral: ∫ sec2(4x + 9) dx

A: Given: ∫sec2(4x+9) dx

Q: Find the indefinite integral by making a change of variables.

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) x(2x + 5)8dx

A: Explained below

Q: Find the indefinite integral. ∫sec3x dx

A:

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: Evaluate the indefinite integral. (Use C for the constant of integration.) x(4x + 7)8dx

A:

Q: Find the indefinite integral.

A:

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

A:

Q: Find the indefinite integral by making a change of variables. ∫x2√(1 − x) dx

A: To determine ∫x21-x dx

Q: Evaluate the indefinite integral. (Use C for the constant of integration. x(8x + 7)8dx

A:

Q: Find the indefinite integral. ∫(x csc2 x) dx

A: Given: ∫xcosec2xdx for finding this integral we will use integral by parts method where, we will use…

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) x(6x + 7)8dx

A: Given:

Q: Evaluate integral of dx/x+2 from -6to-10

A: Given , To Evaluate the integral of dx / x+2 from -6 to -10

Q: Find the indefinite integral. ∫sec4x dx

A:

Q: Find the indefinite integral by making the appropriate change in the variable. a) Sx²Vx³ +1 dx 1+4x…

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 x+ 6x2 + 9x +8

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

Q: Use substitution method to evaluate the definite integral fore dx

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 by making a change of variables. ∫x√(3x − 4) dx

A: To evaluate ∫x3x-4dx

Q: Find the indefinite integral by making a change of variables

A: We have to integrate by making change of variable for the function: ∫11+2xdx In change of variable…

Q: Find the Indefinite Integral by making a change of varlab of Integration.) dx

A: Given: I=∫xx-6dx    ....1 Let, u=x-6⇒x=u+6 Now differentiate on both sides with respect to x.…

Q: Evaluate the indefinite integral: ∫(8x − 4e5−2x) dx

A: Given: Let I=∫8x-4e5-2xdx To Find: To evaluate the given integral.

Q: Find the indefinite integral by making a change of variables. (Use C for the constant of…

A:

Q: Evaluate the definite integral below. 8. 4 -x + 3 3 dx V2x2 + 2x + 4

A: Given,          ∫2383x+432x2+2x+43dx

Q: Find the indefinite integral by making a change of variables.                                  ∫(x2…

A: Let the given integral be y - y = ∫x2-12x-1dx              ......................(1)Let,t2 = 2x-1…

Q: Find the indefinite integral by making a change of variables. |(x + 6)V5 - x dx

A: Given integration is : ∫x+65-xdx To find the value of given integral

Q: Evaluate the indefinite integral 7X+17 (x+2) (x+3) dX

A:

Q: Evaluate the integral. 12x – 9 - dx = x2 + lx – 6 4 -

A: Given, Evaluate ∫4512x-9x2+1· x-6dx

Q: Evaluate indefinite integral: dx / (x+3) * squareroot of x2+6x

A:

Q: Determine the indefinite integral. 25 dx x In 7x 25 S= Sx157x x In 7x dx =

A:

Q: Find the indefinite integral by making a change of variables. 1 √ 4 + ²√2x² dx

A:

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

A: Given,            ∫x+3x2+6xdx

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

A: To evaluate ∫x2+2x+3x3+3x2+9xdx

Q: ((x^3+5x^2-4)/x^2)dx

A: ∫x3+5x2-4x2dx Expand we get  ∫x3+5x2-4x2dx==∫ x+5-4x2dx Apply the Sum Rule:  ∫fx±gxdx=∫fxdx±∫gxdx =∫…

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: Find the indefinite integral of Jsec²x tanx√1 + tanx dx. 22/2

A:

Q: 5. x3 + 2x – 6 dx x4 + 2x2

A:

Q: find the indefinite integral by the change of variable ∫ x²√1-x

A:

Q: Find the indefinite integral by making a change of variables. ∫x√(x + 6) dx

A: The given integral is ∫xx+6dx

Q: Find the indefinite integral ∫sech23x dx

A:

Q: dx V5 + 4x – x²

A: Integrate