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Substitution of 'u=1+sin(x)' is required.Differentiating this with respect to x gives cos(x)... therefore du=1/cos(x) dxmultiplying that through leaves the integral of sin(x)(1+sin(x))^3 which therefore c...

To solve this problem we will use a clever substitution to easily integrate and thus obtain the answer.First we can represent tan(x) as its fractional equivalent sin(x)/cos(x), assigning the variable u to...

First, we need to remove one of the variables from one of the equations. In this case, we multiply the first equation by 4 to give 12x+4y=28.Then minus the 2nd equation from this to give 10x+0y=20.Now div...

Take a right angled triangle with hypotenuse of length 1, and angle at the bottom of the hypotenuse equal to x. We will let o denote the length of the side opposite the angle, and a denote the length of t...

The first step is to find dx/dy in terms of y, which when differentiating comes out as 3/2cos(y/2), so dy/dx in terms of y is the reciprocal of this.The next step is to eliminate the y dependent terms, wh...