Evaluate the integral
x4 – 2x2 + 4x + 1
x3 – x2 - x + 1
dx

Looks like the integral is

First simplify the integrand by long division (or however you like):

Also notice that

Split the last term into partial fractions:

So the integral is equivalent to

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.

tangent

step-by-step explanation: