Look at the given expression,

(2x-1.1 + 0.5x0.5 + 2ex)

dx

The first rule to remember is this: constant coefficients such as the 2 in front of the x^-1.1 always "go along for the ride." In other words, we can just copy them over when taking the antiderivative (see below).

First term:

2x-1.1

dx.

Since the 2 "goes along for the ride," we can write

	2x-1.1	dx	=	2 x-1.1 dx	=	2 x-0.1 -0.1 + C	Using the power rule. (-1.1+1 = -0.1)
			=	-20x-0.1 + C

That takes care of the first term. The second term is

	0.5x0.5 dx	=	0.5 x0.5 dx	The 0.5 "goes along for the ride"
		=	0.5 x1.5 1.5 + C	Power rule for integrals
		=	x1.5 3 + C

The last term is

	2ex dx	=	2 ex dx	The 2 "goes along for the ride"
		=	2ex	ex is its own antiderivative

Putting them all together gives:

(2x-1.1 + 0.5x0.5 + 2ex)

dx

=

-20x-0.1

+

x1.5 3

+ 2ex + C

You can enter this as -20x^(-.1) + x^1.5/3 + 2e^x + C

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