Question

Hi, please solve this below antiderivatives ( integration) questions. Thanks

Find the antiderivative using proper symbolism ( BIG S and dx) Show detail steps

1- ln( e )^ x squared

2- sinx cosx

3- cos x / sin x

4- 3x ^ 3 - 4 x ^ 2 + 7x. + pi

5- ( sec x ) ^ 2 tanx

6- 3 ^ 1/2 - 4 x ^ -2

7- ( 2x ^ 2 - 8x ) ( 2x -4

8- sin 5x cos5x

9- ( 2- x) ^ 3/5

10- x ^ 3 - x ^ -3

11- e ^2

Answer #1

1. Evaluate the following indefinite integrals using integration
by parts. Show your work please:
a) ∫ x^2 * e^3x dx
b) ∫ x sin 5x dx

Find the antiderivative
f(x) = 3x^2 + 4x + 5
f(x) = 3 cos x
f(x) = e^2x + 4x^3
f(x) = sec^2 x

1- Find the solution of the following equations. For each
equation, 2- determine the type of the category that the equation
belongs to.
1. y/x cos y/x dx − ( x/y sin y/x + cos y/x ) dy = 0
2. x(1 − y^2 )dx + y(8 − x^2 )dy = 0
3. (x^2 − x + y^2 )dx − (e^y − 2xy)dy = 0
4. 2x sin 3ydx + 3x^2 cos 3ydy = 0
5. (x ln x −...

Solve:
a) 3log2(5x+1)+4=1
b) logx+log(3x+1)=1
c) 43x-1=8x
d) 5ex^2-2-12=24.94528049
e) ln((7x+1))-ln(x2+x-1)=0.69314718

Evaluate the integral using integration by parts with the
indicated choices of u and dv. (Use C
for the constant of integration.)
xe5xdx; u
= x, dv =
e5xdx
2. Evaluate the integral. (Use C for the constant of
integration.)
(x2 + 10x) cos(x) dx
3. Evaluate the integral. (Use C for the constant of
integration.)
cos−1(x) dx
4. Evaluate the integral. (Use C for the constant of
integration.)
ln(
x
) dx

Answer each of the questions below. (a) Find an equation for the
tangent line to the graph of y = (2x + 1)(2x 2 − x − 1) at the
point where x = 1. (b) Suppose that f(x) is a function with f(130)
= 46 and f 0 (130) = 1. Estimate f(125.5). (c) Use linear
approximation to approximate √3 8.1 as follows. Let f(x) = √3 x.
The equation of the tangent line to f(x) at x =...

13. Consider
f(x)=sqrt x-2
a) Using any of the three limit formulas to find f ′ ( a
), what is the slope of the tangent line to f ( x )at x = 18? (6
points execution, 2 points notation)
b) Find the equation of the tangent line at x =
18
14. State the derivative.
a) d/ d x [ x ^n ]
b) d /d x [ cos x ]
c) d /d x [ csc...

Find the derivative of the function.
(a) f(x) = e^(3x)
(b) f(x) = e^(x) + x^(2)
(c) f(x) = x^(3) e^(x)
(d) f(x) = 4e^(3x + 2)
(e) f(x) = 5x^(4)e^(7x+4)
(f) f(x) = (3e^(2x))^1/4

PLEASE SOLVE ALL 8 QUESTIONS SHOWING STEP-BY-STEP
SOLUTIONS.
Solve for the unknown variable on the interval 0 is (less than
or equal to) x (less than or equal to) 2pi.
1. 4 cos^2 x - 3 =0
2. Square root of 2 sin 2x = 1
3. 3cot^2 x-1 = 0
4. cos^3 x = cos x
5. sin x - 2sin x cos x = 0
6. 2sin^2 x- sin x-3 = 0
7. csc^2 x- csc x -...

Find the most general antiderivative of the function. (Check
your answer by differentiation. Use C for the constant of
the antiderivative.)
f(x) = 4x
+ 7
f(x)=
Find the most general antiderivative of the function. (Check
your answer by differentiation. Use C for the constant of
the antiderivative.)
f(x) =
9
x8
f(x)=
f '(t) = sec(t)(sec(t) + tan(t)), −− π/ 2
< t < π/ 2 , f ( π/ 4) = −3
f(t)=
Find f. f '''(x) = cos(x), f(0)...

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