HELP PLEASEEEE ASAP

Question

Find the following antiderivatives.

1. -3dx

2. x^2/3dx

3. √xdx

4. 5x^3dx

5. ((√x)/x)dx

6. x⁵dx

7. 2x^⅓dx

8. 1/(5√x²)dx

9. 3/2x³dx

10. 2x/(√x)dx

Answer 1

1 S-3dx = -3Sdx = -3x + C C= a constant, "S" is my symbol for integral, as my keyboard doesn't have the more conventional integral symbol, which does stand for "sum" like an S and looks very similar to an S.

2 Sx^2/3dx = (1/3)Sx^2dx = (1/3)x^3/3 + C = (x^3)/9 + C

asuming you meant (x^2)/3. but if by chance you meant x^(2/3), then

Sx^(2/3)dx = 3x^(5/3)/5 + C

3 Ssqrxdx = (2sqrx^(3/2)/3 + C

4 Ssqrx(^3)dx = Sx^(3/2)dx = (2x^(5/2))/5 + C

5 Ssqrx/xdx = Sx^(-1/2)dx = 2x^(1/2) + C = 2sqrx + C

6 Sx^5dx = x^6/6 + C

7 2Sx^(1/3)dx = 6x^(4/3)/4 +C = 3x^(4/3)/2 + C

8 S1/5sqxdx = (1/5)Sx^(-1/2)dx = (1/5)2sqrx + C = 2sqrx/5 + C

9 S3/2x^3dx = (3/2)Sx^-3dx = (3/2)x^-2/-2 + C = -3/(4x^2) + C = -0.75/x^2 + C

10 S2x/sqrxdx = 2Ssqrxdx = 2x^(3/2)/3/2 + C = 4x^(3/2)/3 + C