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Show that (x + 1)(x + 2)(x + 3) can be written in the form ax3 + bx2 + cx + d where a, b, c and d are positive integers.

(x+1)(x+2) = ( x^2 + 3x + 2) - multiplying out the first 2 terms(x^2 + 3x + 2)(x + 3) = x^3 + 3x^2 + 2x + 3x^2 + 9x + 6 - multiplying the product of the first two terms by the last termx^3 + 6x^2 + 11x + ...

Answered by Rachel K. • Maths tutor

6352 Views

Integrate exp(2x)cos(8x) by parts

Let u=exp(2x) and v'=cos(8x)From these you can obtain u' and vu=2exp(2x) and v=1/8 sin(8x)Formula: integral(uv'dx)=uv-integral(vu'dx)=1/8 exp(2x)sin(8x)-integral(1/4 sin(8x)exp(2x))=1/8exp(2x)sin(8x)+1/16...

Answered by Chloe D. • Maths tutor

3364 Views

Solve the equation 8x^6 + 7x^3 -1 = 0

The first thing to recognise is this is a quadratic in disguise, therefore we can rewrite the equation in terms of a new variable y.
Where y=x³
The equation then becomes 8y²

Answered by Kelan P. • Maths tutor

7062 Views

Integrate sinxcosx dx

Since the question is a trigonometry question, we shall use integration by recognisation, in which case, we found out that the derivative of sin x is cos x.Therefore by chain rule, we can integrate the fu...

Answered by Harris L. • Maths tutor

4285 Views

Find the values of x where x^(2) + 4x + 4 = 0

To solve this question we need to find the values of x which work for the equation x^(2) + 4x + 4 = 0. To solve the equation we can factorise the left-hand side into brackets which will m...

Answered by Ben A. • Maths tutor

7170 Views