- Determine the indefinite integral : In(x³) dx.

Q: Calculate the integral in terms of the inverse hyperbolic functions.

A: To make the answer in inverse hyperbolic form, do the following substitutions. Substitute x=sint in…

Q: Evaluate the indefinite integral, ſx² sinh x³ dx.

A: To evaluate: I=∫x2sinh x3dx⇒I=∫sinh x3  x2dx

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) | (in(x))6 dx х

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Q: Use a table of integrals to evaluate the definite integral.

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) (In x)7

A: This is a basic integration problem

Q: Use a change of variables to evaluate the following indefinite integral. dx

A:

Q: Find the indefinite integral. (Use C for the constant of integration.)

A: Given integral is I = ∫7 (t5 - t3 + 1) dt First we have to integrate the given integral equation.…

Q: r" (tan (x)) (In (cos(x))) dx

A: solve this integration by substitution. substitue                    ln(cos(x)) = t on solving

Q: Evaluate the indefinite integral. V 16 +x² dx %3D to

A: We need to integrate ∫16+x2x4dx

Q: In x dx

A: Given,            ∫ln (x)x dx

Q: evaluate the indefinite integral.

A:

Q: Evaluate the integrals

A:

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

A:

Q: Use substitution to find the indefinite integral

A: Given, ∫2+lnxx dx

Q: Find the indefinite integral. (Use C for the constant of integration.) xp J xV81 - (In x)²

A: The given integral is ∫9x81-(ln x)2dx. The integration of 1a2-x2=sin-1xa+c, where c is constant.

Q: Find the indefinite integral using the substitution x = 2 tan θ.

A: Then integrate with substitution

Q: Find the general indefinite integral. (Use C for the constant of integration.) x' dx

A:

Q: Calculate the integral in terms of the inverse hyperbolic functions.

A: Calculate the integral in terms of the inverse hyperbolic functions.

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sin(In 16x) dx

A:

Q: Evaluate the indefinite integral given below. [6e¹tan (2) Gett 6e4 tan (2x) sec² (2x) dx

A: The given integral: ∫6e4 tan2xsec22xdx

Q: Use the Table of Integrals to evaluate the integral.

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) de cos(e) -

A: The solution of given problem is follows as

Q: -1)*dx

A: Given  ∫02(x-1)2 dx

Q: Find the general indefinite integral using definition. х5 + 3х — Vx + dx X.

A: we need to evaluate the integral,∫x5+3x-x+1x dx

Q: Evaluate the indefinite integral: 3 dx J x In(5x)

A:

Q: Find the general indefinite integral. (Use C for the constant of integration.) dx

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) an(x) In cos(

A: The given integral is: I=∫9tan xlncos x dx

Q: Find the general indefinite integral. (Use C for the constant of integration.) - 3u4 ته( ل u? +)

A: This question can be solved by using some basic formulas of integration like ∫xndx

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) [ (In(x))²6 dx X

A: topic- indefinite integral

Q: Find the general indefinite integral. (Use C for the constant of integration.) / (2x² + * + dx x2 +…

A:

Q: e`1/x - dx x2

A:

Q: dt

A: We have to find indefinite integral

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) dt

A: To find ∫ t5e-t6dt

Q: Verify the following indefinite integral by differentiation.

A: Given: ∫xdxx2-12=-12x2-1+c for verifying given integral, we differentiate R.H.S. with respect to x

Q: Evaluate the indefinite integral. x² dx 1 + x6

A: To find :- Integral of ∫x2/(1+x6)       ........................(1)   Solution :- According to the…

Q: Evaluate the indefinite integral.

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) dt 9 + tan(t) CoS

A:

Q: Use a table of integrals to evaluate the definite integral.

A: We have to evaluate the definite integral using table of integrals: ∫03x2+16 dx Rewriting the…

Q: Evaluate the indefinite integral. V6 + x°dx + C

A: Evaluate ∫x56+x6dx

Q: Find the indefinite integral. (Use C for the constant of integration.) dx

A:

Q: Use a table of integrals to find the indefinite integral

A: To integrate: ∫lnxx3+2lnxdx Let substitute t=3+2lnx.  t=3+2lnxdtdx=0+2xdt2=dxx Substituting the…

Q: Find the general indefinite integral. (Use C for the constant of integration.)

A:

Q: Find the indefinite integral using the substitution x = √x√4 + x² dx + C 2 tan(0)

A: SOLUTION-

Q: Evaluate the integral. x² + 25 dx of

A:

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

A: Given an indefinite integral

Q: Find the indefinite integral -dx (2-x ²)? dx = 2-x)?

A: To find the indefinite integral:∫x2-x22dx

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sin dx

A:

Q: s(3x)dx, u=3X Scos(3) dx =?

A: We use substitution method to solve the integration.

Q: Find the indefinite integral r 2(In(x))³ dx .

A: In some cases an indefinite integral can be simplified to a standard integral using an appropriate…

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) cos(In(5t)) dt t

A: Evaluate the integral: I=∫cosln5ttdt