How do you use substitution to integrate xx+4dx?

2 Answers
Jul 29, 2015

The process is outlined below.

Explanation:

We are to evaluate, x(x+4)12dx.

We shall accomplish this by substitution.

Let, (x+4)=t
dx=dt (By simple differentiation).

Thus, the integral becomes,

x(x+4)12dx=t4t12dt

=t12dt4t12dt

=23t328t12+C, where C is the integration constant.

In terms of x, the integral may be now written as,

x(x+4)12dx=23(x+4)328(x+4)12+C.

Aug 15, 2017

xx+4dx=23(x+4)x+48x+4+C

Explanation:

xx+4dx=x+44x+4dx,
xx+4dx=x+4(x+4)124(x+4)12dx,
xx+4dx=(x+4)124(x+4)12dx,
xx+4dx=23(x+4)328(x+4)12+C