Integration Techniques

[chris sawan]

I've got a homework packet tonight dealing with integration techniques. I need some help with where to start on some various integration problems. I haven't been able to even figure out the first step, so if you could help me with them I would greatly appreciate it.

Integrate x^2+3x+7/square root of X

I don't know if I should use substitution or anything here, or take out the square root of X and then just integrate.


Integrate (tan^4x)(sec^2)x

I know that the anti-derivative of sec^2x is tanx but im not exactly sure what I should do about the tan^4x

any help would be appreciated
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[Daniel_Feldman]

For the first problem, simple break it up since you have root(x) as a common denominator. Remember: (x^2+3x+7)/root(x)=(x^2/root(x))+(3x/root(x))+(7/root(x))


For the second problem: You know that the antiderivative of sec^2(x) is tanx...so the derivative of tan(x) is sec^2(x).

So let u=tan(x) and go to work.