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Cornpvtr thr following mtjral X1 _ | dx x3_X2_4x+4...

Question

Cornpvtr thr following mtjral X1 _ | dx x3_X2_4x+4

Cornpvtr thr following mtjral X1 _ | dx x3_X2_4x+4



Answers

Find the following integrals. $$\int x \sqrt[3]{2 x+1} d x$$

They want us to compute this indefinite Integral. Now, the first thing that might help is to rewrite this using a little bit of algebra. And this would be integral of X to the negative 1/2 power DX cause remember, square roots or half powers. And then when we have won over something that's really a negative power. And to integrate this, we would just use the power rule for integration. So remember, we're going toe add one to its power. So that was going to be X to the 1/2. And then we want to divide by our new power. So one, huh? And then plus C and we can use a little bit of algebra now to rewrite this as well. So one over 1/2 is the same thing is multiplying by two and then next to the 1/2 power is just root, ex. So this is what we get when we value

In the question we're calling abound. Untidy real video expert and t X getting cut you the expert and that's one off and plus one plus a constancy in this question were given the entirely river the on the X Times X square the X notice that the first time we can do will be We combine them together you get expert, read the X And now we can identify the three he will be in in this formula so we could get a go to the expert and will be in the three now plus one hour three plus one plus a constancy. It would simplify. We get equal to the expel far off a far plus a constancy.

In this question here what we call abound. Untidy. Who would you of the Expo and the X? Getting close to the expert and this one off and plus one plus a constancy in discussion here were given the integral of the X squared with the x X. You noticed that we can rewrite this inside him as an ex by our three out of two the X And now we can identify. This one will be the end in the formula. The forget record to the X power three out of two plus one if anyway, three add up two plus one plus a constancy. It was similar for Uganda X power. This one will be five out of two. Well, even number five then with him still here plus a constancy and this will be the answer.

The given integral is integration of one minus X and the road X. Dx. Let us start by first simplifying the integrated us. We can multiply the root expert, one minus X. To get under root x minus x rays to the park. Three divided by two dx. We can rewrite the antique villas X rays to the part one divided by two minus x rays. To the part three divided by two dx. Now breaking this integral into two parts we get integral x rays to the part one divided by two. The x minus integral off x rays to the part three divided by two. The X. The first integral simplifies to give x rays with the part three divided by two, all divided by three divided by two minus x rays. To the par five divided by two, all divided by five divided by two plus a constant of integration. Capital C. This can be further simplified Us two divided by three x rays to the part three divided by two minus two, divided by five x rays to the par five divided by two. Let's see. So this will become the final answer


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