What's the integral of x^2 +3/x, with respect to x?

A: x3/3 + 3ln(x) + A.

Step-by-step solution:

Integral (x2+3/x dx) =

[as integrals preserve sums]

integral (x2 dx) + integral (3/x dx) =

[raise exponent by one, multiply by the reciprocal, add a constant]

x3/3 + C + integral (3/x dx) =

[3 is a constant, so we we can take it out of the integral. The anti-derivative of 1/x dx is ln(x)+D, which is a standard result you need to know]

x3/3 + C + 3(ln(x) + D)=

[merge the constants into one constant]

x3/3 + 3ln(x) + A.

MG

Related Maths A Level answers

All answers ▸

solve the inequality x^2+4x-21>0


What are the most important trig identities we need to know?


f(x)=2x^3-7x^2+4x+4, prove that (x-2) is a factor and factorise f(x) completely


Show that the curve with equation y=x^2-6x+9 and the line with equation y=-x do not intersect.