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First, recognise that 3^2 = 9. Recall the rule for multiplying indices, that (a^b)^c = a^{bc}. Then, substitute 3^2 in place of 9 to get 3^{4x} = (3^2)^{(x-1)/2}. Use the rule for multiplying indices, so tha...

Finding f(x) requires integrating the function f'(x), because f(x) is the integral of the given function f'(x). So {integralsymbol} f'(x) dx = {integralsymbol} (3x^2 - 5cos(3x) + 90) dx = x^3 - (5/3)sin(3x) ...

This thing we have to solve is an inequality and the solution we are looking for is an entire range of real number, something like "every x between 1 and 2", for example. To do this we need to buil...

Using LATEX (Logarithms, Algebra, Trigonometry, Exponential and Complex numbers) to determine which variable is du and which is dv/dx. This is decided by using the above acronym. For example in this question...

Steps: Use the auxiliary equation on the equation given in the question Solve the resulting equation Identify the appropriate complementary function from the solutions Determine an appropriate particular int...