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The formula for integration by parts is Integral(udv/dx)dx = uv - Integral(vdu/dx)dx
You use integration by parts when you have an integral where you have to terms multiplied together ie Int...

16y³ + 9x²y - 54x= 0 
a) Differentiate the terms separately dy/dx(16y³ + 9x²y - 54x) = dy/dx(16y³) + dy/dx(9x²y) - dy/dx(54x) ...

0.5Ln(x^2+2)+ C

firstly, x² + 4 = 0 x² = -4 x = 2i x = -2iSecondly, x² + 8x + 25 = 0 using the quadratic formulae: x = (-b +- sqrt(b² - 4ac))/2a x = (-8+-sqrt(64-100))/2 x = -8...

To find dy/dx, the differential, of any function... you must times the coefficient of each variable of x by its power, then reduce the power by one. Using this information we can work out that 3x^4 turns ...