Solving the Integral of ((x^2) + 1)^2

[Sidthewall]

Homework Statement

How to find the integral of ((x^2) + 1)^2


My calc background.

I just started learning calc for the summer, so I making or missing little mistakes and i don't have an instructor to point it out to me. I see that some calc questions for me are easy such as the integral of x((x^2) + 1)^2,,, but for some strange reason I can't do ((x^2) + 1)^2.

The Attempt at a Solution

When I see this problem i couldn't find it anything to subsitute which is why i can't solve it, so I need a step by step way to solve this PLZ

 

[Gib Z]

You don't need to substitute, just expand it.

 

[Sidthewall]

K but the question said to use substitution

 

[Sidthewall]

and what if i had ((x^2) + 1)^10, there must be a way to do it w/o expanding

 

[Gib Z]

Okay, then use a Trig substitution. Think of the trig identities you know and decide which substitution would make it look like one of them. You can use the expansion for any powers of n, even large, whilst substitutions makes it very difficult for larger exponents.

 

[Sidthewall]

Okay, then use a Trig substitution. Think of the trig identities you know and decide which substitution would make it look like one of them. You can use the expansion for any powers of n, even large, whilst substitutions makes it very difficult for larger exponents.

K so I am thinking let u = (sinx)^2 + (sinx)^2 + (cosx)^2

 

[Gib Z]

Try u=tan x.

 

[Mark44]

K so I am thinking let u = (sinx)^2 + (sinx)^2 + (cosx)^2

?