Since

**u**= x + 1, d**u**= dx and x =**u**- 1. Bo**u**nds: If x = 0, then**u**= 0 + 1 = 1. If x = 1, then**u**= 1 + 1 = 2. Therefore, ∫(x = 0 to 1) x^2 √(x + 1) dx = ∫(**u**= 1 to...1 Answers · Science & Mathematics · 27/07/2010

∫ (x²)√(x + 1) dx = ? Let

**u**= x + 1. Then: d**u**/dx = 1 d**u**= dx And (s**u**btracting 1 from...)√(**u**) – 2**u**√(**u**) + √(**u**)] d**u**= ∫ [**u**^(5/2) – 2**u**^(3/2) +**u**^(1/2)] d**u**= (2/7)**u**^(7/2) – 2(2/5)**u**^(5/2) + (2/3)**u**^(3/2) + C = (2/7)**u**^(7/2) – (4/5)**u**...3 Answers · Science & Mathematics · 27/07/2010

Let v be any vector in R^3 then for

**u**=[-3,0,3]^T there exist a vector**u**_perp(v) such that: i.) v = a**u**+ b**u**_perp...the solution. Take the dot product of (i) with respect to**u**: <**u**,v> = a <**u**,**u**> + b <**u**,**u**_perp> = a...2 Answers · Science & Mathematics · 11/04/2011

... "a" is a constant and the integral is taken from

**u**=0 to**u**=a. (That is from x=a to x=0, but "x" is...2 Answers · Science & Mathematics · 29/06/2011

You should know that

**U**(28) is an abelian group of order phi(28), where phi is...there are any number of ways to see that**U**(28) is not cyclic. One is to compute the order...2 Answers · Science & Mathematics · 30/03/2012

Let

**u**(x, y) = X(x) Y(y). Substituting this into the ...for some C ==> Y = Ce^(25y^2/2). Therefore,**u**(x, y) = (A cos(5x) + B sin(5x)) * Ce^(25y^2/2...2 Answers · Science & Mathematics · 31/07/2015

Rewrite this as dv/du = (2 + v/

**u**)/(1 + 2v/**u**). Hence, this is a homogeneous DE. So, let v...we solve by separating variables: (1 + 2z) dz/(1 - z^2) = 2 du/**u**==> (-1/2) (1/(z + 1) + 3/(z - 1)) dz = 2 du/**u**, by partial fractions ==>...1 Answers · Science & Mathematics · 20/09/2014

**U**and V are vectors,**U***T is the dot product...5 Answers · Science & Mathematics · 29/02/2008

...rewrite it as: ∫ sec²(e^x) e^x dx = let: e^x =

**u**differentiate both sides: d(e^x) = d**u**e^x dx = d**u**...θ + 1)] sinθ cosθ dθ = let: (sin²θ + 1) =**u**differentiate both sides: d(sin²θ + 1) = d**u**...1 Answers · Science & Mathematics · 24/01/2011

first, let:

**u**= 5x + 8 d**u**= 5 dx (1/5) d**u**= dx go ahead and make the first s**u**bstit**u**tion, to get: ∫ (1/5) (15x + 4) / √(**u**) dx now, to get rid of the n**u**merator, j**u**st take what**u**is eq**u**al to and solve for x 5x + 8 =**u**5x + 8 - 8 =**u**- 8 5x =**u**- 8...2 Answers · Science & Mathematics · 12/12/2010