[CLO-2] Evaluate the Indefinite integral by using the substitution rule. S√tan (x) sec²(x) dx 02√cot(x) + C 02 √tan(x) + C O (cot(x)) ³/2 + C (tan(x))³3/2 + C

Q: -4 tan-(x) dx 1 Find (x + 1)2

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Q: Evaluate 5⁰⁰ x dx. -∞ x sin 2x x²+3 0

A:

Q: Using Substitution to Evaluate a Definite Integral Use substitution to evaluate 1 x² (1+ 2x )°dx.

A:

Q: √x² - 4 ·S x dx.

A:

Q: C. h(x) = 2x² sin(x) - x sin(x) – 15 sin(x); ONLY product rule, NO power rule.

A: Given; h(x) = 2x2sin(x) - xsin(x) - 15 sin(x)

Q: In x (1+In x)² 1. S = dx

A: In this question , we will integrate .

Q: 3x2[x18 + x15 sinh(ax³)] dx

A: Given that ∫3x2x18+x15sinh(ax3)dx, 3∫3x2x15sinh(ax3)+x18dx Take u=x3→dudx=3x2,…

Q: sin (x² 3/2 +2)dx

A: See the details solution in below

Q: Evaluate d/dx { In√(x+1)}

A:

Q: dx 1 +X |1- (Tan (x) )2 12

A:

Q: I [20 / (e(8-10x) dx. The integrand equals 20 divided by [e raised to power of (8 - 10x)]. O…

A: ∫ex dx =ex+C

Q: In/cosh(2x)– sinh (2x)): Select one: O 2x None O O

A:

Q: x² 1- x6 dx

A: Explanation of the answer is as follows

Q: Evaluate (i) dx S √e xlnx√(2lnx)² – 1

A: We are asked to evaluate the integral

Q: Evaluate the indefinite integral x5 - 5x dx x3

A: This is a simple question related to integration  Solution is given below

Q: V3 4 dx (tan¯¹ (x)) (1 + x²)

A: ∫134tan-1x1+x2dx