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Let us try to find

in a few different ways

**Using a trig rule**

We have that

therefore

Here we used the fact that

The latter can be verified by taking the derivative of the right-hand side or using the substitution method with *u*=*ax+b*.

**Using the substitution u=sin(x) **

Let us do a substitution

So

**Using the substitution u=cos(x)**

Let’s do the substitution

so

**Using integration by parts**

So

Here we added a constant of integration. We finally get

I.e. the same answer we got with our second method.

Ok, let´s plot the graphs of our three solutions.

You will find that they are simply the same solution shifted up or down with some constant. Given the right values of the respective constant of integration, we can make all three solutions overlap.

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