Versus mods! - Current record: 511

[anoni]

0.

Knowing what they mean and being able to solve them are veeeeeeeeeeeeeeeeeeeeeery different xD

[HyenaKing]

1


tecnhically i can solve them too.
but i'd rather jsut do my sport.

[anoni]

0.
With high school calculus O.o?

Some of those integrals are very difficult to solve I don't think any highschool would teach you that xD

[HyenaKing]

1


I donot think you know that last 2 years i was home-shooled!
and i think i got ahead.
I jsut grabbed the Calculaus and advanced calculaus books and srted larning.
maybe it was above high scool level... But whatever!

[Nicklaus Morgan]

1
I know mine doesn't

[HyenaKing]

2


and then we GOT ABOVE 1!

[Nicklaus Morgan]

3
Wow ... This is like a new record

[anoni]

0.

Well I'd be interested if you solve some of these, if you can solve the first one int (e^{cos(x)^2} *In(x) * cos(x) dx) I'd be very, very impressed!

I can solve a few, here's one I'm pretty sure I can solve

int((7x + 10) / (x - 5)(x² + 2x + 10) dx

First, parfrac it (because we have an irreducable quadratic we'll have to stick with it)

(7x + 10) / (x - 5)(x² + 2x + 10) = A / (x - 5) + (Bx + C) / (x² + 2x + 10)

Multiply both sides by the denominator on LHS

7x + 10 = A(x² + 2x + 10) + (Bx + C)(x - 5)

CASES: First make x = 5

7(5) + 10 = A(25 + 2(5) + 10) + 0
45 = 45A
A = 1

Now, use x = 0
10 = (1)(10) + C(-5)
0 = -5C
C = 0

Last case can be anything, lets just say x = 1

17 = (1)(13) + ( (-4)
17 - 13= -4B
4 = -4B
B = -1

14/7 = 4B
B = 14/28
B = 1/2

Therefore the parfrac is  1/(x- 5) - x/(x² + 2x + 10)

Now we can INTEGRATE each individual parfrac

int (1/x-5)dx is ln(x - 5)
int (-x/x² + 2x + 10) is -1/2(ln(x² + 2x + 10) but in order to get rid of that pesky 2 in the numerator of the integral we can use the inverse tangent equations, to get (1/3)*tan^-1((1/3)*x + 1/3)

So our final integral is

ln(x - 5) - 1/2*ln(x² + 2x + 10) + (1/3)*tan^-1((1/3)*x + 1/3) + C

I only know that because we did Partial fractions last semester and it's one of the things I remember xD

[HyenaKing]

1


i jsut decoded to ingore that because ia am in new yourk BECAUSE OF MY SPERT NOT MATHSTSTSTSS

[Nicklaus Morgan]

2
I won't even try to read that

[anoni]

0.
It took me 7 minutes to do, you've spent much more of that time on the forums, I bet you could spare 7 minutes

[Nicklaus Morgan]

1
But I don't know to read that

[HyenaKing]

2


Peace, its an unicorn.

[anoni]

0.
Alright then

[Nicklaus Morgan]

1
Oh ... That unicorn is quite difficult