# Category: Integration techniques

## Integral of xln(x)

In this post I am going to explain step-by-step how to integrate the function xln(x). We can solve it by using integration by parts (click here if you want to… Read more Integral of xln(x)

## Integral of sin(x)/x from 0 to infinity

Today we have a tough integral: not only is this a special integral (the sine integral Si(x)) but it also goes from 0 to infinity! Since this is a special… Read more Integral of sin(x)/x from 0 to infinity

## Integration techniques | Trigonometric substitution

When none of the techniques you’ve learnt so far (u-substitution 1, 2,3,4 and integration by parts seem to work, you might consider trigonometric substitution. Basically, if you have a function that reminds you of a trigonometric identity, you let that function be equal to the result of the identity, for example cos²x from 1-sin²x, and then differentiate. To make things more clear I’m going to use this example: U substitution and integration by parts are not going to be very helpful. What we are gonna do instead is let x=sin(theta)… Read more Integration techniques | Trigonometric substitution

## Integration techniques | U substitution – part 2

U-substitution is the most common technique used in integration. It can happen, however, that it doesn’t work out, no matter what you try to substitute. You may think of using another technique, like integration by parts, but it’s not always necessary. You realise u-sub is not working when you still see one or more x’s. For example: As you can see, we have an x that we don’t want. At this point you may think about integration by parts, and yes, that’s actually the way to go. The result is… Read more Integration techniques | U substitution – part 2

## Integration by parts | Solution with procedure

Here you will see how to solve these integrals https://atomic-temporary-167386734.wpcomstaging.com/integration-by-parts-exercises/ and check if you got them right! Wait… we have the integral of sin(x)cos(x) again! So this means that and Easy, right? Let’s solve this integral by performing another integration by parts. so we have We can do the same thing we did for the integral of sin(x)cos(x). Therefore, We now know that this is equal to which is equal to The answer is Same thing here; And that’s it! Stay tuned for more integrals. You might find these links… Read more Integration by parts | Solution with procedure