 Hello and welcome to the session. Let us discuss the following question, question says, find the following integrals. We have to find the integral of 2x square minus 3 sin x plus 5 root x dx. First of all let us understand that integral of k1 f1x plus k2 f2x 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 x raised to the power n dx is equal to x raised to the power n plus 1 upon n plus 1 plus c where c is the constant of integration and integral of sin x dx is equal to minus cos x plus c where c is the constant of integration. Now we will use these three expressions as our key idea to solve the given question. Let us now start with the solution. We have to find the integral of 2x square minus 3 sin x plus 5 root x dx. Now using first expression of the key idea we can write this integral as 2 multiplied by integral of x square dx minus 3 multiplied by integral of sin x dx plus 5 multiplied by integral of root x dx. Now we will find out these three integrals. Now from this expression we get integral of x square dx is equal to x raised to the power 2 plus 1 upon 2 plus 1. Using this expression we get integral of sin x dx is equal to minus cos x and using this expression we get integral of square root of x is equal to x raised to the power 1 upon 2 plus 1 upon 1 upon 2 plus 1 plus c. c is the constant of integration. We know root x can be written as x raised to the power 1 upon 2 and integral of x raised to the power 1 upon 2 dx is equal to x raised to the power 1 upon 2 plus 1 upon 1 upon 2 plus 1. Now this term can be written as 2 upon 3 multiplied by x cube multiplying minus 3 and minus cos x we get plus 3 cos x and here adding these two terms we get 3 upon 2 so it can be written as x raised to the power 3 upon 2 upon 3 upon 2 plus c. Now this expression is further equal to 2 upon 3 x cube plus 3 cos x plus 5 multiplied by 2 upon 3 multiplied by x raised to the power 3 upon 2 plus c. Now 5 multiplied by 2 is equal to 10 so we will write this expression as 2 upon 3 x cube plus 3 cos x plus 10 upon 3 x raised to the power 3 upon 2 plus c. So we get integral of 2x square minus 3 sin x plus 5 root x dx is equal to 2 upon 3 x cube plus 3 cos x plus 10 upon 3 multiplied by x raised to the power 3 upon 2 plus c. This is our required answer. This completes the session. Hope you understood the solution. Take care and have a nice day.