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Evaluate : (i) intx^(9)dx , (ii) int3...

Evaluate :
(i) `intx^(9)dx` , (ii) `int3sqrt(x) dx` ,(iii) `intdx`
(iv) `int1/(x^(2))dx` , (v) `int(1)/(x^(1//3))dx` , (vi) `int5^(x) dx`

Text Solution

Verified by Experts

Using the standard formulae, we have
(i) `intx^(9)dx (x^((9+1)))/((9+1)) + C = (x^(10))/(10) +C`
(ii) `int3sqrt(x)dx = intx^(1//3)dx = (x^((1/3+1)))/((1/3+1)) + C = 3/4 x^(4//3) + C`.
(iv) `int 1/(x^(2)) dx = intx^(-2)dx = (x^((-2+1)))/((-2+1)) + C = - 1/x + C`.
(v) `int(1)/(x^(1//3)) dx = intx^(-1//3) dx = (x^((-1/3+1)))/((-1/3+1)) + C = 3/2 x^(2//3) + C`.
(vi) `int5^(x) dx = (5^(x))/(" log" 5) + C`.
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