Question

1. Integral sin(x+1)sin(2x)dx

2.Integral xe^x dx

3. integral ln sqrt(x) dx

4. integral sqrt(x) lnx dx

Answer #1

Evaluate the following indefinite integral: ∫x^2/√(16+x^2
)dx
Evaluate the following indefinite integral: ∫xe^2x dx

1. the integral of 0 to 1 of (x) / (2x+1)^3 dx
2. the integral of 2 to 4 of (x+2) / (x^2+3x-4) dx

evaluate each indefinite integral
4) \int -(2*csc^(2)2x)/(cot(2x)*\sqrt(cot^(2)2x-1)); u=cot2x
5) \int (10x^(4))/(9+4x^(10)); u=2x^(5)
6) \int (20x^(3))/(\sqrt(25-25x^(8)))
7) \int (1)/(x\sqrt(25-(ln-2x)^(2)))

How come integral -1 to 1 (sqrt (1+x^2)) dx can be the same as
2* integral 0 to 1 (sqrt(1+x^2))dx ??

Evaluate the integral using trig substitution.
definite integral from 1 to sqrt(2) 6 / (x^2 sqrt(4-x^2))dx
(a) write the definition for x using the triangle
(b) write the new integral before any simplification
(c) write the new integral after simplifying and in the form ready
to integrate
(d) write the solution in simplified exact form
write all answers next to the specified letter above

A) Use the Comparison Test to determine whether integral from 2
to infinity x/ sqrt(x^3 -1)dx is convergent or divergent.
B)Use the Comparison Test to determine whether the integral from
2 to infinity (x^2+x+2)/(x^4+x^2-1) dx is convergent or
divergent.

Find derivatives (Please show work!)
1. f(x)=ln(5x^3)
2. f(x)=(ln^3)x
3. f(x)=e^(5x2+2)
4. f(x)=xe^2x
5. f(x)=xlnx

find the indefinite integral.
1.) elongated S dx/x(lnx^8)^9
2.) elongated S 1/x^8/9(3+x^1/9) dx
3.) elongated S √x/√x-4 (4 is not under sq root)
I couldn't figure out how to do the elongated S symbol

Solve the following
a)y=tan^-1 (sqrt((x+1)/(x+2)
b)y=ln(sin^-1(x))
c)d/dx[sec^-1(x)]=1/(x(sqrt(x^2 -1)
d)Find Y' tan^-1(x^2 y)=x+xy^2

integral from -6 to 6 of sqrt(36-x^2)^3 dx

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