Evaluate the integral in which å, b are the derivatives of a, b with respect to t.

Q: |In (x)| dx 00 1+ x2

A: Given integral

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: Use integration by parts to evaluate the integral: In(s)ds

A: Given, To Evaluate

Q: Evaluate the integral or show that it is divergent.

A:

Q: evaluate the given integral.

A:

Q: dx

A: Consider the integral

Q: Evaluate the integral. In(Vx) dx

A: Solution:

Q: Consider the integral (In(x))° dx:

A:

Q: Write as a single integral in the form F(x) dx.

A: Integration is the process of finding the anti-derivative function of the given function. The…

Q: In(x) dx =

A: To find:∫lnxx5dx

Q: Use Cauchy's Integral Formula and Cauchy's Integral Formula for Derivatives, when appropriate, to…

A: Given integral: ∮Ce5izz4-z4z-i3dz closed curve is z=4. Cauchy integral formula: fw=12πi∮Cfzz-wdz…

Q: What change of variables is suggested by an integral containing V100 – x??

A: 100-x2

Q: Find the indefinite integral z/4+z'dz.

A: Given : ∫z24 + z3dz

Q: evaluate the integral (In (X )Ć dx X3

A:

Q: Evaluate the integral in terms of the constant: dx

A:

Q: Use the form of the definition of the integral given in this theorem to evaluate the integral. dx

A:

Q: dx Evaluate the improper integral if it exists

A: The solution is given as follows

Q: Evaluate the integral of (t)(sint)(cost) dt

A: We need to evaluate the following integral ∫tsintcostdt

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

A:

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

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

Q: Use Cauchy's Integral Formula and Cauchy's Integral Formula for Derivatives, when appropriate, to…

A: The given integral is: ∮Cz2+5z2-6iz-5dz, where C is the circle z-6i=1.3 Cauchy Integral formula: Let…

Q: Evaluate the integrals in ∫esec πt sec πt tan πt dt

A: Given: ∫esecπtsecπttanπtdt for evaluating this integral we substitute esecπt=u now differentiating…

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

A:

Q: Evaluate the integral In x dx

A:

Q: Use integration by parts to evaluate the definite integral + dt.

A:

Q: Evaluate the indefinite integral: ∫t−6/11 dt

A: The integral of xn is given by: ∫xndx=xn+1n+1+C   Using the above rule:…

Q: Use the Table of Integrals to evaluate the integral.    ∫et sin (α t- 3) dt

A: To evaluate I=∫et sinαt-3dt

Q: b) Evaluate the integral E (1+ etane) Sec20 de

A:

Q: Evaluate the integral or show that it is divergent.

A: The given integral is ∫1∞dx2x+13. Evaluate as follows.

Q: Evaluate the indefinite integral.   ∫ Sec3t  tan 3 t dt

A:

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

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

Q: dt 5+ t2

A: Given: ∫02t25-t2dt

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 x dx from the definition of RS-integral.

A:

Q: e doe

A:

Q: integral

A: Useful formula: ∫xndx = xn+1/(n+1) + c

Q: Find the indefinite integral z(3 +z) dz.

A:

Q: | tan įx sec? įx dz:

A:

Q: Use the substitution u =x +3 to evaluate the indefinite integral below. dx

A: Given Data: Integrand: ∫2xx2+35dx Substitution: u=x2+3 ......1 The derivative of equation (1) with…

Q: 20. Verify by differentiation that finx dx = x(In x-1) + C, then use appropriate changes of…

A:

Q: to う

A:

Q: dx 1)3/2

A: Given integral

Q: 28. Je sin i dt

A:

Q: Evaluate the integral, if it exists.    ∫0π/4  (1 + tan t) 3 Sec2 t dt

A: Given information: The integral is ∫0π4+tant3sec2t dt  Calculation: Apply the u-substitution method.…

Q: f(x)° f' (x) dx

A: Given, ∫fx3 f'x dx   We have to evaluate the integral in terms of x .

Q: Evaluate the integral. In 2 tanh x dx

A: ∫02tanhx dx=∫02sinhxcoshxdxUsing formula ∫f'(x)f(x)dx = ln|f(x)| +cHere , f(x)=sinhx , f'(x)= coshx

Q: ,3 x2+1 t – t2 dt In(x)

A:

Q: dt t/ 12 1r² – 16

A:

Q: Use a substitution of the form u = ax +b to evaluate the indefinite integral below. V3x +2 dx

A: