Please solve these Intregation?

Question

Please help me I have exam on friday
1) Intregate e^x{(x^2+1)\(x+1)^2}
2) Intregate [{sin x - cos x}\{1 + sin x*cos x}]dx = 0

Answer 1

1-
for [ (x^2+1)/(x+1)^2] carry out the devision:

= 1- 2x/(x^2+2x+1)

Now: the integration cames

Int{ e^x [1- 2x/(x^2+2x+1)] } dx
Int{ e^x - e^x [2x/(x^2+2x+1)] } dx

Now carry the integrtion using Integration by part

2. There is, I think, a trigonometric formula looks like that integral try to find that formula and simplify the function then carry the integration.

Answer 2

For number 1)

e^x - 2*e^x/(x+1) + C

For number 2), you have it set to zero. Are you wanting to solve for x? This is a very difficult integral by the way. Maybe you do it using series expansion rather than traditional techniques.

-1 +2x - (3/2)x^2 +(2/3)x^3 +(5/8)x^4 -.....

Then integrate....

Answer 3

hey its very easy
prob1:
first break up the polynomial parts
then integrate e^x with each of the degrees of x i.e.integration by parts

prob 2:
multiply & divide by sin x + cos x
that's enough

Answer 4

Common you can do it, they are not that hard. I will keep checking and if you don't have the correct answer by Thrusday night, I'll tell you but this is in the head stuff. Worse comes to worse use a TX-88

Answer 5

#1 try integretion by parts

#2 try multiply by conjugate

Answer 6

What happened when you tried to evaluate these integral expressions?

What did you try?