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  1. u = sqrt(7) * sin(t) du = sqrt(7) * cos(t) * dt du / ( u * sqrt(7 - u ^2)) => sqrt(7) * cos(t) * dt / (sqrt(7) * sin(t...sqrt(7)) * (ln|sin(t)| - ln|1 + sqrt(1 - sin(t)^2)| + C u = sqrt(7) * sin(t) u / sqrt(7) = sin(t) (1/sqrt(7)) * (ln| u ...

    3 Answers · Science & Mathematics · 01/05/2013

  2. 1) (x^3) (square root of (x^2 + 1)) dx let u = tan(x). Then du = sec^2(x) dx Identity tan^2(x) + 1 = sec^2... to #1 -------------------------- 2) (x^2) (1 + 2x^3)^5 dx Let u = (1 +2x^3)...............Then du = 6x2 dx and du/6 = dx Now I...

    1 Answers · Science & Mathematics · 27/01/2010

  3. u (x) = s(x)/t(x) then u '(x) = [s'(x)t(x) - s(x)t'(x)] / t(x)^2 u ''(x...t(x)^2 - [s'(x)t(x) - s(x)t'(x)](2)t(x)t'(x)}/t(x)^4 u ''(x) = {[s''(x)t(x)-s(x)t''(x)]t(x)^2 - [s'...

    2 Answers · Science & Mathematics · 24/10/2012

  4. u =√(4-x) u² = 4-x x = 4-u² dx = -2u du So subbing... of your original integral, you now have: ∫(4-u²)( u )(-2u du) = -2 ∫4u² - u ^4) du = -2 (4u³/3 - u ^5/5) + C...

    3 Answers · Science & Mathematics · 25/06/2009

  5. ∫ dx / x sqrt(x+4) u ^2 = x+4 2udu = dx ∫ dx / x sqrt(x+4) = ∫ 2u du / ( u ^2-4) u = ∫ 2 du / ( u ^2-4) = 2 ∫ du/( u +2)( u -2) 1/( u +2)( u -2) = A/( u +2) + B/( u -2) 1 = A( u -2) + B( u +2) equate the...

    2 Answers · Science & Mathematics · 06/08/2010

  6. u = 8i + 7j → tan( u ) = 7/8 v = 7i - j → tan(v) = - 1/7 tan(a - b) = sin(a - b) / cos(a - b...tan(b)] / [1 + tan(a).tan(b)] → adapt this result to your case tan( u - v) = [tan( u ) - tan(v)] / [1 + tan( u ).tan(v)] tan( u - v) = [(7/8) - (- 1/7...

    2 Answers · Science & Mathematics · 29/04/2019

  7. A U B = { n ∈ N : 3 or 5 divides n } (A U B...not divide n } B^c = { n ∈ N : 5 does not divide n } A^c U B^c = { n ∈ N : either 3 or 5 does not divide n } So the...

    2 Answers · Science & Mathematics · 03/06/2012

  8. Let u = 1 + 3x^3 Then du/dx = 9x^2............(simple differentiation) So du = 9x...gt; dx = du/9x^2................(divide both sides by 9x^2) Substitute u = 1 + 3x^3 and dx = du/9x^2 to obtain ∫[2 to 4] x^2 (1+3x^3)^2 dx = ∫[2 to 4...

    2 Answers · Science & Mathematics · 16/10/2016

  9. sin( u ) = 4/5 = y/z x^2 + y^2 = z^2 x^2 + 4...x^2 = 25 - 16 x^2 = 9 x = 3 1) cos( u ) = x/z = 3/5 <==== positive since... to take the positive root. sin( u /2) = + √( (1-cos u )/2 ) sin( u /2) = √( (1- (3...

    3 Answers · Science & Mathematics · 17/08/2011

  10. sec [ arctan( u ) + arccos(v)] let arctan( u ) = A tan A = u ==> opposite side = u and adjacent side = 1, hypotenuse = √( u ^2 + 1) sin A = u / √( u ^2 + 1) ------(1) and cos A = 1 / √( u ^2 + 1...

    1 Answers · Science & Mathematics · 27/07/2010

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