# What is the antiderivative of #(16 - x)^(3/2)#?

##### 1 Answer

Jan 29, 2016

#### Explanation:

Antiderivative is just the integration. For handling this type of problem, you should be comfortable with the power rule.

#color(red)(intquad x^n dx = x^(n+1)/(n+1)+C#

Our problem we have to find

#intquad(16-x)^(3/2) dx#

We shall use a

Let

Differentiating with respect to

#-dx= du#

#dx=-du#

Our integral now becomes

#intquadu^(3/2)(-du)#

#=-intquad u^(3/2)du#

Use the power rule

#=-u^(3/2+1)/(3/2+1) +C#

#=-u^(5/2)/(5/2)+C#

#=-2/5u^(5/2)+C#

Substituting back for

#=-2/5(16-x)^(3/2) + C#