We want to compute the integral tan e dx. If we use integration by parts, with u(x)=tan-lr and v'()=1, what do we get? tan x - x· tan x dx 1 dx 1+ x? - 1+ x? dx 1+ x? x tan r - 1 x tan x - dx 1+ x2

Q: Which of the following cannot be evaluated directly by a basic integration formula? ver Vex - 1 dx…

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Q: 3. Find the integral (a) f(cos(x) + sin(x))² cos(2x) dx 1/3 /tan(x) (b) dx sin(2x) tan-¹(x) dx (d)…

A: (a)  I=∫cosx+sinx2cos(2x)dx =∫(cos2x+sin2x+2sinxcosx)cos(2x)dx =∫(1+sin2x)cos(2x)dxHere, Let…

Q: Determine the integral of the ff. functions. 1. S - 10 sin 5x dx 2. S 4 x cos x² dx 3. S sec 2 (3x +…

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Q: Can the integrations in (a) and (b) both be correct? Explain. dx V1 – x² sin- x + C a. dx dx b. =…

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Q: x dx = b2 - . T/2 cos(x) dx = 1, together with the properties of definite integrals, to evaluate…

A: To calculate the integral using the given formulae

Q: 3. Find the following definite integrals. (2x +3)dx (x2- 1)dx x² - 2x)dx sin(3x + 4) dx 1

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Q: Evaluate the following integrals: 1. S(cos x + csc² x)dx 2. S(tan x + sec² x)dx 3. S(1+sec²x)dx 4.…

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Q: Evaluate using Integration by Parts. x sin(3 – x) dx (Use symbolic notation and fractions where…

A: Given: ∫xsin(3-x)dx

Q: In the integration of (cos y)^2 dy/(1 - sin y), what is the first step to solve the integral?…

A: ∫cosy21-siny dy

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) | Vx19 sin(4 + x21/2) dx…

A: Since the exact one wasn't specified we'll answer the first question only. Please resubmit a new…

Q: Find the indefinite integral. (Use C for the constant of integration.) | (2 cos x + 9 sin x) dx

A:

Q: 2. When applying the formula for integration by parts, how do you choose the u and dv? How can you…

A: Choose u for logarithmic, inverse, algebraic, trigonometric and exponential function and the others…

Q: For evaluating the integral x tan-lr dx, we apply integration by parts technique with the…

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Q: (4)Evaluate the definite integral (a)[ 1+sin x dx (b) | 2t + cost dt -7/2 5 x + dx (d)[ sec' 0 d0…

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Q: Find the indefinite integral. (Use C for the constant of integration.) (4 cos x + 3 sin x) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 9 cos X dx 3 + sin x

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Q: Determine the following integrals: 1.1 G 3x³ +8 X dx 1.2 G 1.3 4x+6 dx x + 3x-10 sec² (sin 5x)cos 5x…

A: We have to find out solution

Q: (sec2 x + csc2 x)cos2 x dx

A: Given: I=∫sec2x+csc2xcos2xdx   Use the trigonometric identity; 1). sinx=1cscx 2). cosx=1secx And…

Q: In the integration of (cos y)^2 dy/(1 - sin y), what is the first step to solve the integral? Select…

A: Given integral.

Q: Find the value of the definite integrallo 2 cos ( x ) dx given that the antiderivative for the…

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Q: Evaluate the integral. dx 9-x2 O sin-1 cos 1*+c O cos Cos 7 O 2 2 cos'1를x*C Sin 1

A: SOLUTION-

Q: Which of the following integrals is NOT appropriate for a substitution method? A 5x*sin(x³)dx ®…

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Q: Evaluate the integrals sin2.x -dp- J(5 + cos2.x) e) 3

A: Since, you have asked multiple question, we will solved the first question for you. If you want any…

Q: Find the indefinite integral. (Use C for the constant of integration.) (4 cos x + 7 sin x) dx

A: Given the integrationI=∫(4cosx+7sinx)dx

Q: Find the indefinite integral. sinh(4 - 7x) dx Step 1 First, let u = 4 - x. Now, differentiate u with…

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Q: Find a suitable method for integration of Sin (x²) x = 0,√ using a two-point sample of Sin (x²) x =…

A: We have to find the integration I=∫0πsinx2dx let f(x)=sinx2 For ∫abf(x)dx, two point formula is…

Q: A-Evaluat wing integrais: 1) S (cos x / sin? x) dx. 2) S (2x+4)/3 dx, use x-0 to x=2. 3)…

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Q: Find the integral. (Use C for the constant of integration.) sin(-3x)cos(2x) dx

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Q: Find the general indefinite integral. (Use C for the constant of integration.) (Sx² + 8 +) dx 4 x2 +…

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Q: Evaluate the integral (1+lnx)5/ x dx from 1 to e.    Find the indefinite integral: sin(x)…

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Q: How do I calculate the indefinate integral of e^sinx(cos(x))dx

A: Given integral is ∫esinxcosxdx

Q: Find the indefinite integral (use c for the constant of integration) ∫cos3 x sin x dx

A: To solve the given integral

Q: Use integration by parts to evaluate the integral. 6 3 e cos x dk 0

A: Given integral is

Q: Find the indefinite integral. (Use C for the constant of integration. sin 4x sin 3x dx sin x sin 7x…

A: Solution is given in step 2

Q: Find the indefinite integral using integration by parts with the given choices of u and dv. |x…

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Q: Pat made the substitution x – 4 = 5 sint in an integral and integrated to obtain f (x) dx = 12t – 2…

A: integrate

Q: Find the indefinite integral. (Use C for the constant of integration.) S sin(3æ) sin(2x)da O +(3…

A: we have to use  2sin A sin B = cos(A-B)-cos(A+B) And solve the integration.

Q: Ql: Find the integration of : 1. S cos (3 sin x)cos (4 sin x). cosxdx

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Q: Suppose you use r = V5 tan (0) to make a substitution when evaluating an integral. After integration…

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Q: Find th Integral. for the constant of Integration. |(7 cos(x) – 2 sec?(x)) dx

A:

Q: . Consider the integral f sin ¹x dx. If we let u = sin-¹x and dv = dx, the integral can be written…

A: answer is in next step

Q: Evaluate the integral (i) S3x3 sin 4x dx (ii) ſ In (x³ + x) dx (ii) cot-1 2x dx (iv) ſeax cos bx dx

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Q: Find the general indefinite integral. (Use C for the constant of integration.) sin 2x 9. dx sin x

A: Explanation of the answer is as follows

Q: Find the indefinite integral. (a) / (2* + v#)dx (c) / 2x6 + x5 -dx x4 (4) [(4cs (xỉ + 5x + 4)dx (4…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: 2) Perform the integration dx i) S x/1-(In x)² dx ii) S 4e2x-1 Find th doriuotiuo

A: As per bartleby guidelines we only give first questions answers.

Q: Consider the integral /sin-'(5æ) dæ: dx: Applying the integration by parts technique, let -1 sin(5æ)…

A: We have to solve the integral

Q: o integrals are equivalent and (b) calculate 2. | sin(t) dt = sin(x + 1) dx %3!

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Q: Evaluate the integral. (Use C for the constant of integration.) 9 sin(2x) dx 1 + cos“(x)

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Q: 5. Evaluate the definite integral (1+lnx)² dx а. 1 dx. b. -1 2x+3

A: Explanation of the answer is as follows

Q: Find the indefinite integral. (Use C for the constant of integration.) (5 cos x + 7 sin x) dx

A: ∫5cosx+7sinx dx∫5cosx dx+∫7sinx dx