Find the indefinite integral. (Note: Solve by the simplest method-not all require integration by parts. Use C for the constant of integration.) t In(t + 3) dt

Q: In the given equation as follows , use a table of integrals with forms involving ln u to find the…

A: Let I=∫x2-6x+2x3+2x2+xdx. First, factors the denominator x3+2x2+x. Use the identity a2+2ab+b2=a+b2.…

Q: 2. Find a) ³ dx b) xdx. Hence, find whether the following integrals exist and, if they do, find…

A: To evaluate the given improper integrals

Q: B. Solve the following integrals. 1.) ²(x + 1)dydx

A:

Q: Solve the following integral using substitution method: X S. dx √x²-1

A:

Q: 1/6 dx 3.S T1-9x2

A: Solve the definite intregal

Q: x - 1 dx x² +1Xx– 2)

A: First of all use partial fraction then differentiate.

Q: In the given equation as follows , use a table of integrals with forms involving ln u to find the…

A:

Q: Find the indefinite integrals, if possible, using the formulas and techniques.

A:

Q: Find the definite integral of S, (2x + x2) dx

A:

Q: Find the indefinite integral.

A: Formulae used: aman=am-n1an=a-nddxex=ex∫xndx=xn+1n+1+C

Q: In the given equation , select the basic integration formula you can use to find the indefinite…

A:

Q: 1 t cos 4t² dt 2

A:

Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Show step by step solution. 1. dx

A: see below the answer and calculation with steps

Q: Q2: Solve the following integrals: (3) dx

A:

Q: dx I = е. a² +x²

A:

Q: ++y = 1- u (t– n); y (0) =1, y(0)' = -1

A:

Q: x² /16 – x²dx

A:

Q: (h) d.x e* + 1 (i) g³ – 1 d.r (j) d.x x² + 5

A:

Q: a) S In Gxt1) dx 2.

A: In this question we have to find the Integration. Formula Used, - Chain Rule. - ∫lnx=1x+C

Q: Evaluate the definite integral. 2 e 1/x5 dx х5

A: The given definite integral is,

Q: (d) (x² + 1)² dx (e) L dx (x² + 1)² (f) eir dx

A: d. Given

Q: dx. х2 + 4 3.

A:

Q: Solve the following integrals using the appropriate technique/s of

A:

Q: xV|x² – 9| + 7 dx

A:

Q: Find the indefinite integral of 1/3 e x dx

A: Given indefinite integral is: I=∫13exdx We have to integrate the above with respect to x.

Q: state what method applies and how one applies it, but do not evaluate the integral:

A: Degree of the numerator =2 Degree of the denominator = 1 Since the degree of the numerator is more…

Q: Find the indefinite integration of 9t8 +(t/8)

A:

Q: Use the appropriate technique of integration to solve the following. (a) In x? + 1dx

A: SOLUTION-

Q: Find the indefinite integral of t/1+t

A: Here we have to find the indefinite integral of t/(1+t) .

Q: - ydy (y + 1) - J y + 1

A:

Q: x + 4 dx = x' + 4x

A: Given, ∫x+4x3+4xdx Now we take the partial fraction we get, x+4x3+4x=Ax+Bx2+4…

Q: 1 dx = 4 + x

A: To findI=∫19+x24dx

Q: Find the indefinite integrals, if possible, using the formulas and techniques.

A: (a) To integrate: ∫ex2dx We know that, ex=1+x+x22!+x33!+⋯⋯=1+x+x22+x36+⋯⋯ Now, ex2=1+x2+x42+x66+………

Q: 2.S x² -4 X -dx

A: Note: Asper company guidelines, we are supposed to answer the first question only. Kindly ask the…

Q: find formulas for the functions represented by the integrals.

A:

Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Show step by step solution. 1. dx 2. x²/4-x?

A:

Q: (а) 4x³ dx -2 (b) | (2г° — Зг + 6) de (c) | (2г — Зг + 6) de

A:

Q: 00 e-st cosh t dt

A:

Q: 2e" dx (e – 1)2 1

A:

Q: Væ +1 dx

A: Substitute u=x+1,du=dx2x+1. Here if u=x+1⇒x=u2-1.

Q: 4) Evaluate the definite integral: s?(2n² - 4x + 8)dx. |

A:

Q: Given |(-2x° + 3x – 3x° – 6)dx, evaluate the indefinite integral. Do not include +C in your answer.…

A: Integral x^n is x^(n+1)/(n+1)

Q: In3 (1 – x)el×l dx solve this integral without integration by parts.

A:

Q: Find the indefinite integral. 17 dx +C

A:

Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Show step by step solution. dx

A:

Q: Solve the following Integral Equation: -t + x(0) = 3 %3D

A:

Q: 2.x dx +1, x'

A: Let I is the value of given Integral.

Q: х+1 dx 3 2 2 25 - x

A:

Q: T/2 sin & cas Ode sinte

A:

Q: 3-Evaluate the integrals (a) Log X up leg, (ar) kp C da

A: