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Integral(Sin[x]Cos[x]dx) can be calculated. The method is to recognise that the trigonometric identity of 2Sin[x]Cos[x]=Sin[2x] can be applied. This would transform the integral into Integral(0.5Sin[2x]) ...

First rearrange the equation dy/dx = x³ + 5x Then move the dx to the RHS of the equation dy = ( x³+ 5x)dxThen integrate both sides, with respect to y on the LHS and with respect to x...

This is a simple differentiation example of a polynomial, where one uses the the standard algorithm - i.e.[nx^n-1] Ina polynomial, one differentiates all parts separately. First Take 3x^2. Multiply by the...

We can find dy/dx by using the product rule: If y=uv then dy/dx = u (dv/dx)+ v (du/dx). In this question u= sin(6x) and v= sec(2x).So du/dx= 6cos(6x) and dv/dx=2sec(2x)tan(2x), using our rules for differe...

To differentiate xcos(2x), you first have to use the product rule, because this function is two functions (x and cos(2x) multiplied togetherNow you have x*(cos(2x))'+cos(2x)To differentiate cos(2x) you ha...