More maths help! Integration

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Revision for my upcoming maths exam is going well but I'm so stuck on a question! Any help would be majorly appreciated.

Integrate the following with respect to x:

a) x^2 + cos x

b) e^2x - 4

I've tried googling the question hoping to find examples but I've come up with nothing.

a) 1/3x^3 + sin x + c

b) 1/2e^2x - 4x + c

Which bits are you struggling with? Not sure where to offer help!

Golden thanks!

When we covered this I totally got it but I seem to have lost it since!

I know its a very big ask but would you be able to break it down for me? If I can work through the steps it would massively help...

When adding or subtracting then the functions can just be integrated as is. Is only if they are multiplied or a function of a function where you will need to separate or apply a rule.

Thank you Badwifey

For the x^2 we are going up a power so we multiply by 1/(new power) and then change the 2 to a 3

Google table of standard integrals

For powers of x: add one to the power...then divide by the new power.

There will be a table of derivatives for sin, cos etc

As these functions are added or subtracted, you can just work through each in turn.

Powers of x: for any axn, you need to first add 1 to the power, and then divide the multiplier by your new power, to give (a/(n+1))x(n+1)

So in your example, a=1, n=2: so n+1=3 and a/(n+1) = 1/3

Answer is 1/3x^3 + c

Integral of cos x is sin x - to be fair this is one to learn.

Integral of ex is ex; for eax the integral is (1/a)eax. In your example a=2, so answer is 1/2e^2x + c.

Integral of a constant a is just ax + c. So your example of 4 integrates to 4x + c.

As the functions are added or subtracted, each can be integrated individually and then added or subtracted in turn. Plus c at the end!

Omg thank you all so much! This has really helped.

Golden That is exactly what I needed. Thank you