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Question Number 54259 by 951172235v last updated on 01/Feb/19

Commented by Meritguide1234 last updated on 01/Feb/19

Answered by rahul 19 last updated on 01/Feb/19

$$1.$$$$I=\int (x^{3m}+x^{2m}+x^m){(2x^{2m}+3x^m+6)}^{\frac{1}{m}}dx$$$$I=\int (x^{3m-1}+x^{2m-1}+x^{m-1}){(2x^{3m}+3x^{2m}+6x^m)}^{\frac{1}{m}}dx$$$$put2x^{3m}+3x^{2m}+6x^m=t$$$$\Rightarrow 6m(x^{3m-1}+x^{2m-1}+x^{m-1})dx=dt$$$$\Rightarrow I=\frac{1}{6m}\int {\left(t\right)}^{\frac{1}{\mathrm{m}}}\mathrm{dt}$$$$\Rightarrow I=\frac{m+1}{6}{(2x^{3m}+3x^{2m}+6x^m)}^{\frac{m+1}{m}}+C.$$

Commented by rahul 19 last updated on 01/Feb/19

thank you sir!��

Commented by Meritguide1234 last updated on 01/Feb/19

$$\mathrm{good}\mathrm{rahul}$$

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