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All we do here is break down into three parts: x², 6x & 1.x² becomes 2x as we multiply by the power and then decrease the power by one.6x becomes 6 and 1 becomes 0.So alltogether...

first notice the integral is in the form f'(x)/f(x), and indefinite integrals of this form are ln|f(x)|+c.
therefore the integral is [ln|x⁴+x|] between limits 1 and 2.
subbing in li...

Differentiating the above equation with respet to y:dx/dy = m;Substituting the value of m in the given form:x = (dx/dy) y i.e. the solution is(dx/dy) y - x = 0

Find the positive value of x such that log_x64 = 2
Using the logarithm rules, we know that we can rearrange the given equation into the form:
x² = 64
Knowing this, we s...

First, we need to realise that we will be using the trigonometric identity sin(x)² + cos(x)² = 1
As our goal is to end up with an equation involving only sin, we will therefore ...