 Hello and welcome to the session. Let us discuss the following question, questions raise. Find the following integrals. We have to find the integral of 2x minus 3 cos x plus e raise to the power x dx. First of all, let us understand that integral of k1 f1x plus k2 f2x. And plus k3 f3x dx is equal to k1 multiplied by integral of f1x dx plus k2 multiplied by integral of f2x dx plus k3 multiplied by integral of f3x dx, where k1, k2 and k3 are real numbers. Also integral of cos x dx is equal to sin x plus c, where c is the constant of integration and integral of e raise to the power x dx is equal to e raise to the power x plus c, where c is the constant of integration and integral of x raise to the power n dx is equal to x raise to the power n plus 1 upon n plus 1 plus c, where c is the constant of integration. Now we will use these four expressions as our key idea to solve the given question. Let us now start with the solution. Now we have to find integral of 2x minus 3 cos x plus e raise to the power x dx. Now using expression first of the key idea, we can write this integral as 2 multiplied by integral of x dx minus 3 multiplied by integral of cos x dx plus integral of e raise to the power x dx. Now we will find these three integrals. Integral of x is equal to x raise to the power 1 plus 1 upon 1 plus 1, here value of n is 1. So we will use this integral given in expression 4 of the key idea to find integral of x dx, here value of n is 1. So integral of x dx is equal to x raise to the power 1 plus 1 upon 1 plus 1. Now integral of cos x dx is equal to sin x, so we can write here 3 sin x and integral of e x dx is equal to e x and c is the constant of integration. Now this expression can be further simplified as 2 multiplied by x square upon 2 minus 3 sin x plus e raise to the power x plus c, 2 and 2 will get cancelled and we get x square minus 3 sin x plus e raise to the power x plus c. So we get integral of 2x minus 3 cos x plus e raise to the power x dx is equal to x square minus 3 sin x plus e raise to the power x plus c, where c is the constant of integration. This is our required answer. This completes the session, hope you understood the solution. Take care and have a nice day.