Find the following integral. Note that you can check your answer by differentiation. / (t+ 1)? t2 dt =

Q: Evaluate the following integrals.

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Q: Calculate the following definite integral: |x² – 1| dx -2

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Q: Integrate the following using ~2 x+1 2. dx

A: ∫12x+1xx-1dx

Q: Evaluate the following indefinite integral. Use C for constant of integration. * cos(10x) + sin(20x)…

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Q: 4. dx (x² +1)*

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Q: Evaluate the following integrals: dx

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Q: Find the indefinite integral- cos t dt sin t

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Q: Find the following indefinite integral. +2e -0.1x dx

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Q: Evaluate the following integrals. (a) /* sin(x)dx

A: Goven : Inetrgal ( x2 sin(x))dx

Q: Evaluate the definite integral: 4 dx 0 x2+16

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Q: Evaluate the definite integral.

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Q: Find the indefinite integrals: x5/2 + 4x + 1 dx a) / ? b) / (a" 6t7 2 + Te' ) dt t3

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Q: V A

A: ∫x1+x2dx=∫2u4+u2du=2·∫u4+u2du=2·∫2v24+v4dv=2· 2·∫v24+v4dv=2· 2·∫ -v4v2+2v+2+v4v2-2v+2dv=2·…

Q: Find the derivative of the following integrals: (a) (**at) (b) (LA dt) Vt +1

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Q: Find the following indefinite integrals. X dx= Vx6 +C

A: Given,

Q: Vex – 1 dx c2

A:

Q: Evaluate the definite integral. 1 6 cos(at/2) dt

A: Given:        ∫016cosπt2dt Taking constant out      =6∫01cosπt2dt substitute u=πt2…

Q: 4 dx X-X-2Ą

A:

Q: dx x-1 4

A: Here we take the substitution x-1 = u to solve this integration.

Q: t. ト ニ

A: We can solve them to find dy/dx as below

Q: dx. х2 + 4 3.

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Q: /2+In x dx

A:

Q: Evaluate the integral: square root of x cos(1+ x to the 3/2 power) dx

A: Evaluate the integral

Q: dx 3 x (1+ Vx)²

A: according to our guideline we are supposed to answer only the first question if you want any…

Q: Evaluate the following integral or state that they diverge.

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: x Inx dx .2 4. dx 4-x2 3.

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Q: Find the following indefinite integral - 3r – 5x + 18 dx x² – 6

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Q: 1 dx = 4 + x

A: To findI=∫19+x24dx

Q: dx

A:

Q: S sin x dx dx

A: 1. ∫0∞sinxdx     [-cosx]0∞ -[cos(∞)- cos(0)]ans =1 2. ∫0∞dxx(x+1)dx Substitute u=√x ⟶ du/dx=1/2√x…

Q: Find the indefinite integral.∫(cos5 t/√sin t)  dt

A: Given information: The indefinite integral is ∫cos5tsintdt Trigonometric identities used:…

Q: Evaluate the definite integral. 25 10e V X dx 0/

A: We use substitution method

Q: Find the following integral. Note that you can check your answer by differentiation. | t(t4 – 6)* dt…

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Q: Evaluate the integral 3 sin(t)dt

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Q: Evaluate the definite integral on the interval [0, pi/4] sin(t) / cos^2(t)  dt

A: By substitution, we calculate the value of given integral.

Q: S xe2x*sin(e**)dx

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

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Q: ex dx V1 - e2x

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Q: Evaluate the definite integral V9 – x dx 0.

A: ∫05 x9-xdx

Q: Væ +1 dx

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

Q: The definite integral sec (4x)e dx is equal to:

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Q: Find the indefinite integral. 17 dx +C

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Q: Evaluate the following integrations: 3. dx 1 1+x2

A: Since you have posted multiple question in this question so I have solved first question as per our…

Q: Evaluate the definite integral. e 1/x dx

A: Now consider,

Q: Find the indefinite integral. cos t dt sin t

A: Consider the given indefinite integral, ∫cos5tsin tdt use the trigonometric identity, cos2x=1-sin2x…

Q: х — 1 dx 2?(а + 1) 1

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Q: Determine the following indefinite integral. dx |( + x7) dx= O

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Q: Evaluate the following integral 1 dx (x – 5)²(x + 3) a

A: We have to evaluate the given integral    The given integral is   ∫1(x-5)2(x+3)dx

Q: Calculate the following integrals. dx (a)

A: Note:  As per our guidelines, we are supposed to answer only one question. Kindly repost other…