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Question Number 123967 by Algoritm last updated on 29/Nov/20

	Answered by TANMAY PANACEA last updated on 29/Nov/20
	$t^6 =x+2 ∫(t/(t^2 +t^3 ))×6t^5 dt ∫((6t^4 )/(1+t))dt 6∫((t^4 −1+1)/(t+1))dt 6∫(((t^2 +1)(t+1)(t−1)+1)/(t+1))dt 6∫t^3 −t^2 +t−1+(1/(t+1)) dt 6{(t^4 /4)−(t^3 /3)+(t^2 /2)−t+ln(t+1)}+c put t=(x+2)^(1/6)$
	$t^{6} = x + 2$ $\int \frac{t}{t^{2} + t^{3}} \times 6 t^{5} d t$ $\int \frac{6 t^{4}}{1 + t} d t$ $6 \int \frac{t^{4} - 1 + 1}{t + 1} d t$ $6 \int \frac{(t^{2} + 1) (t + 1) (t - 1) + 1}{t + 1} d t$ $6 \int t^{3} - t^{2} + t - 1 + \frac{1}{t + 1} d t$ $6 {\frac{t^{4}}{4} - \frac{t^{3}}{3} + \frac{t^{2}}{2} - t + l n (t + 1)} + c$ $p u t t = {(x + 2)}^{\frac{1}{6}}$
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