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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...

All we need to do here is find the values of x that make each bracket zero.So2x-4=02x=4x=2andx+1=0x=-1

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

Using the trignometric principles,sin (ACB) = AB/AC = 3/6 = 1/2Thus, angle ACB = 30 degreesand angle BAC = 90 - angle ACB = 60 degrees

x²+8x+15 = (x+3)(x+5)So, the value of x²+8x+15 is zero when x²+8x+15 = 0 i.e. x = -3 or x = -5.