Evaluate using the tabular method shown in the notes.integral 5x4ex dx __________ +C Integration by TablesSo far in this chapter, you have studied several integration techniques that can be usedwith the basic integration rules. But merely knowing how to use the various techniquesis not enough. You also need to know when to use them. Integration is first andforemost a problem of recognition. That is, you must recognize which rule or techniqueto apply to obtain an antiderivative. Frequently, a slight alteration of an integrand willrequire a different integration technique (or produce a function whose antiderivative isnot an elementary function), as shown below.Salmx2In x2x In x dx+ CIntegration by parts4In xdx(In x)?+ C2Power Rule1dx = In|In x| + CIn xLog Ruledx = ?In xNot an elementary functionMany people find tables of integrals to be a valuable supplement to the integrationtechniques discussed in this chapter. Tables of common integrals can be found inAppendix B. Integration by tables is not a "cure-all" for all of the difficulties that canaccompany integration-using tables of integrals requires considerable thought andinsight and often involves substitution.Each integration formula in Appendix B can be developed using one or more ofthe techniques in this chapter. You should try to verify several of the formulas. Forinstance, Formula 41du(а + bu)?иа+ Inla + bu| ) + CFormula 4b2(а + bucan be verified using the method of partial fractions, Formula 19Ja + bududu= 2Ja + bu + aFormula 19uJa + buиcan be verified using integration by parts, and Formula 841du 3D и — In(1 + en) + CFormula 841 + eucan be verified using substitution. Note that the integrals in Appendix B are classifiedaccording to the form of the integrand. Several of the forms are listed below.(a + bu)Ja + buu"(а + bu + cu?)(a? + u?)u?Ju + a?Ja?Trigonometric functionsInverse trigonometric functionsExponential functionsLogarithmic functions EXAMPLE 1Integration by TablesdxFind1Solution Because the expression inside the radical is linear, you should considerforms involving Ja + bu.аS:a + bu+ CduarctanFormula 17 (a

Question

Evaluate using the tabular method shown in the notes.integral 5x4ex dx  __________ +C Integration by TablesSo far in this chapter, you have studied several integration techniques that can be usedwith the basic integration rules. But merely knowing how to use the various techniquesis not enough. You also need to know when to use them. Integration is first andforemost a problem of recognition. That is, you must recognize which rule or techniqueto apply to obtain an antiderivative. Frequently, a slight alteration of an integrand willrequire a different integration technique (or produce a function whose antiderivative isnot an elementary function), as shown below.Salmx2In x2x In x dx+ CIntegration by parts4In xdx(In x)?+ C2Power Rule1dx = In|In x| + CIn xLog Ruledx = ?In xNot an elementary functionMany people find tables of integrals to be a valuable supplement to the integrationtechniques discussed in this chapter. Tables of common integrals can be found inAppendix B. Integration by tables is not a &#34;cure-all&#34; for all of the difficulties that canaccompany integration-using tables of integrals requires considerable thought andinsight and often involves substitution.Each integration formula in Appendix B can be developed using one or more ofthe techniques in this chapter. You should try to verify several of the formulas. Forinstance, Formula 41du(а + bu)?иа+ Inla + bu| ) + CFormula 4b2(а + bucan be verified using the method of partial fractions, Formula 19Ja + bududu= 2Ja + bu + aFormula 19uJa + buиcan be verified using integration by parts, and Formula 841du 3D и — In(1 + en) + CFormula 841 + eucan be verified using substitution. Note that the integrals in Appendix B are classifiedaccording to the form of the integrand. Several of the forms are listed below.(a + bu)Ja + buu&#34;(а + bu + cu?)(a? + u?)u?Ju + a?Ja?Trigonometric functionsInverse trigonometric functionsExponential functionsLogarithmic functions EXAMPLE 1Integration by TablesdxFind1Solution Because the expression inside the radical is linear, you should considerforms involving Ja + bu.аS:a + bu+ CduarctanFormula 17 (a < 0)a +bu- aaLet a = – 1, b1, and u = x. Then dudx, and you can writedx2 arctan /x – 1 + C.1EXAMPLE 2Integration by Tables•••D See LarsonCalculus.com for an interactive version of this type of example.Find9 dx.Solution Because the radical has the form Ju? – a?, you should considerFormula 26.lu/u - a² – a Inlu + Vu – a²) + Cu?a² duLet u = x? and a = 3. Then du2x dx, and you have%3D9 dxV)2 – 32 (2x) dx- 9 – 9 In? + JA* – 9) + C.EXAMPLE 3Integration by TablesEvaluatedx.1 + e-x²Solution Of the forms involving e&#34;, consider the formulaSidu%3D и — In(1 + е&#34;) + С.Formula 841 + e&#34;Let u = -x². Then du =- 2x dx, and you have- 2x dxdx+1 + e¬x?- – In(1 + e¬*)] + cx2= [ + In(1 + e=*)) + c.So, the value of the definite integral is* + In(1 + e¬*³) | = 14 + In(1 + e-4) – In 2] = 1.66.dx1 + e

Accepted Answer

Find the integral

Evaluate using the tabular method shown in the notes. integral 5x4ex dx __________ +C