integrate

1. xsinx dx
1+cos2x

2. √(x-1)(x-2)(x-3 dx

10 Answers

39
Dr.House ·

the first one can be done by integration by parts.

39
Dr.House ·

sinx/cos2x on multiplying and dividing this by cos2x, then we get tanxsecx/sec2x+1

this one can be solved by taking sec2x=t.

now i think the sum is done.

as in the problem integration by parts is x(∫ sinx/cos2x+1) +∫1∫ sinx/(cos2x+1)

1
voldy ·

for second put x=t2+2 think this should be enough for this problem then it reduces to a std integral I think.

39
Dr.House ·

wat about first one? is it correct?

62
Lokesh Verma ·

bhargav I dont see 1 being solved by that substitution.. :(

11
Subash ·

isnt the second one discontinuous

can its indefinite integral still be found

11
Anirudh Narayanan ·

1 can be rewritten as -x.d[log(1+cosx)]

And then taking -x as first function and integrating by parts, we get:

-x. log(1+cosx)+∫log(1+cosx)dx

Then????

62
Lokesh Verma ·

subash you are right....

But I think indefinite integral can still be found.
When we put the limtis, we have to be careful.

take for example y=√x(1-x)

these can be integratd but are not defined for all R.

62
Lokesh Verma ·

anirudh.

I couldnt solve the secodn part of that integral.

:(

39
Dr.House ·

ya bhaiyan sorry. i took the soln in wrong way. we cant solve it by that.

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