 Hello and welcome to the session. The given question says, evaluate integral 2x into tan inverse x square divided by 1 plus x raised to the power 4 into dx. Let's start with the solution. So we have to integrate 2x into tan inverse x square divided by 1 plus x raised to the power 4 into dx. Let us denote y at tan inverse x square. Now I know that derivative of tan inverse y with respect to y is equal to 1 divided by 1 plus y square. On differentiating both sides with respect to x, we have on the left hand side dy divided by dx and on the right hand side we have 1 divided by 1 plus x square whole square into derivative of x square with respect to x. And this is equal to 2x divided by 1 plus x raised to the power 4. Therefore dy is equal to 2x divided by 1 plus x raised to the power 4 into dx. Let us denote the given integral by 1. So 1 with the help of dy and y can further be written as integral 2x divided by 1 plus x raised to the power 4 into dx contributes to dy and tan inverse x square is y. So we have to find integral y into dy and this is equal to y square divided by 2 plus a constant c. Now let us substitute the value of y which is tan inverse x square. So here we have tan inverse x square whole square divided by 2 plus a constant. This is further equal to half tan inverse x square whole square plus a constant. Thus on evaluating the given integral we get the answer as half into tan inverse 2x whole square plus a constant. So this completes the session. Bye and take care.