Question

integration of integral
2x√x dx​

Answer 1

(i) 2a2b2 + 5ab2 + 8a2b2 – 3ab2

= 2a2b2 + 8a2b2 + 5ab2 – 3ab2

= 10a2b2 + 2ab2

(ii) 4a + 3b – 2a – b

= 4a – 2a + 3b – b

= 2a + 2b

(iii) 2xy + 4yz + 5xy + 3yz – 6xy

= 2xy + 5xy – 6xy + 4yz + 3yz

= 7xy – 6xy + 7yz

= x + 7yz

(iv) ab + 15ab – 11ab – 2ab

= 16ab – 13ab = 3ab

(v) 6a2 – 3b2 + 2a2 + 5b2 – 4a2

= 6a2 + 2a2 – 4a2 + 5b2 – 3b2

= 4a2 + 2b2

(vi) 8abc + 2ab – 4abc + ab

= 8abc – 4abc + 2ab + ab

= 4abc + 3ab

(vii) 9xyz + 15yxz – 10zyx – 2zxy

= 9xyz + 15xyz – 10xyz – 2xyz

= 24xyz – 12xyz = 12xyz

(viii) 13pqr + 2p + 4q – 6pqr + 5pqr

= 13pqr + 5pqr – 6pqr + 2p + 4q

= 12pqr + 2p + 4q

(ix) 4ab + 0 – 2ba

= 4ab – 2ab + 0 = 2ab

(x) 6x2y – 2xy2 + 5x2y – xy2

= 6x2y + 5x2y – 2xy2 – xy2

= 11x2y – 3xy2

Answer 2

Answer:

$\\\tt \dfrac{4}{5} x^{(\frac{5}{2})}$

Step-by-step explanation:

$\\\tt \int\limits{2x \sqrt{x} } dx \\\\\tt \int\limits{2x^{\frac{3}{2} } } dx$

For integration we use:

$\\\tt \int\limits{x^{n} } dx \\= \dfrac{x^{n+1}}{n+1}$

Using this,

$\\\tt { \dfrac{2x^{(\frac{5}{2} )} }{\frac{5}{2} } } dx \\\\\\\tt = \dfrac{4}{5} x^{(\frac{5}{2})}$