# integrate

1. ### Integral of (cosx+sinx)^2dx

I did this but not sure if it is correct: ∫(cosx+sinx)^2dx= ∫(cos^2x+2cosxsinx+sin^2x)= ∫(2cosxsinx)= 2∫cosxsinx= 2sinx-cosx+C <--------End
2. ### Solve for k

P =(197.3e^(197.3kt))/(e^(197.3kt) + 1) Solve for k, assuming it is a linear function of P
3. ### Integrate dP/dt =kP

Integrate dP/dt = kP solving for P? And how do I find k if it is a constant?
4. ### Integrate and Differentiate f(z)= 1/x^(2)

Hi I am working on a question that simply states: Differentiate and Integrate the following functions... ..f(z)= 1/x^(2) If I am meant to differentiate with respect to z then do either: (i) leave the x term as it is; (ii) not include the x term as differentiating with respect to z does not...
5. ### Was asked to integrate: "x ln(x)" by parts, but my answer ≠ the textbook's?

I was asked to integrate: "x ln(x)" by parts and received the following answer: ln(x) (x^2 / 2) - (1 / x) (x^2 / 2) + c. However, the answer in the back of the book is: "ln(x) (x^2 / 2) - (x^2 / 4) + c. Why is the term to the right of the minus sign different in the book's answer?
6. ### integrate 0.25(e^-2x)(sec x )

i have tried , but eventually , i got back the same form as the question.... what's wrong with it?
7. ### integrate -x (sinx )(e^2x)

is it possible to integrate -x (sinx )(e^2x) ??
8. ### integrate sinx (e^2x)

my ans is 2(e^2x)sin x / 3 - (4/15)(cosx )(e^2x) , is it correct ?
9. ### integrate dv / srt rt ( 1 +v^2)

is it wrong to integrate dv / srt rt ( 1 +v^2) = ( (1+v^2)^0.5) / (2v)(0.5) ?
10. ### Re: integrate ln(tanx+1)

how to solve this?????
11. ### integrate sin2x cos4x

why the final ans that i get is = 0 ? which part of my working is wrong ?
12. ### integrate using hyperbolic substituition

is my method correct ?
13. ### integrate by substituition

i have done this question in 2 ways , but i gt stucked ... for the trigonometric substituition , how should i proceed form there ? for the hyperbolic substuition , how should i proceed ?
14. ### integrate (x^3)(cosh2x)

why the ans from the tabular method is different from the by part method ? why the ans from for each term of tabular method is more than the by part method by 1/2 ?
15. ### integrate 1/ sqrt rt ( 1-e^(2x) ) using trigonometry substituition

how to integrate 1/ sqrt rt ( 1-e^(2x) ) using trigonometry substituition ? How should I start ? i know that for sqrt rt (a^2 -x^2 ) , i should use asinθ
16. ### integrate

$\int_{surd 2 }^{2} 1/(x^2)($\sqrt{x^2 -1}$dx$ I'm asked to solve this question using trigonometry substitution , i gt stucked here , how should i proceed?
17. ### Integrate (e^(3t) - 3) / (e^(3t) - 9t +9) from 0 to 1

I know that I need to somehow use substitution, integration by parts, or completing the square in order to be able to work with this. However, I have no idea where to begin. Should I try substitution to start? If so, what's the best choice for u?
18. ### Integrate (x^2 + 5) / (x^2 +1) dx

Do I need to use the complete the square technique to solve this problem?
19. ### Integrate x / (x+1)^3

Hello, Could you help me with this? Integrate x / (x+1)^3 from a=1 to b=4. I don't think that substitution works here, so my idea was to approach this using integration by parts. I tried solving it with u=(x+1)^-3 and dv = x, but that didn't work out because I ended up with something that I...
20. ### integrate 1/( x ( sqrt rt (x2 -1 ) ) ) from √2 to 2

i gt it = arc sec x , then i sub √2 and 2 inside , i gt an error , why is it wrong ?