Top answers

a) Find the indefinite integral of sec^2(3x) with respect to x. b) Using integration by parts, or otherwise, find the indefinite integral of x*sec^2(3x) with respect to x.

a) First deduce that problem can be solved by inspection. Then use the fact that the derivative of tan3x equals 3sec^2(3x) and adjust for the constant. (Note this fact should be given in a formula booklet).b...
ER
Answered by Ebrahim R. • Maths tutor
4171 Views

How do you integrate the natural logarithm?

We already know that the derivative of ln(x) is 1/x, so how can this be used for integration?Recall integration by parts uses knowledge of the derivative of one of the parts in the formula.int(u v' dx) = uv ...
JL
Answered by Josh L. • Maths tutor
3589 Views

solve x^3+2x^2+x=0

factorise x 3 +2x 2 +x=0 => x(x 2 +2x+1)=0 => x(x+1)(x+1)=0 => x(x+1) 2 =0 => This leads to x=0 and (x+1) 2 =0 so x=0 and x+1=0 => Giving us the answer x=0,-1
RR
Answered by Robbie R. • Maths tutor
6045 Views

Using the sum, chain and product rules, differentiate the function f(x) = x^n +x^3 * sin(1/[3x])

The following function consists of the sum of two variables x^n and x^3 * sin(1/[3x]). Let's break the differentiation down term by term and differentiate x n first since it's the easier term. Recalling the ...
VS
Answered by Valeri S. • Maths tutor
3451 Views

Calculate the indefinite integral of ln(x)?

This would be calculated using the integration by parts method: NOTE: You can consider the function ln(x) to be a constant of value 1 multiplied by ln(x). The question would then become: Calculate the indefi...
UO
Answered by Uwais O. • Maths tutor
5114 Views