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sin-101x-sinx-99-dx-




Question Number 82617 by necxxx last updated on 23/Feb/20
∫sin (101x)(sinx)^(99) dx
$$\int\mathrm{sin}\:\left(\mathrm{101}{x}\right)\left({sinx}\right)^{\mathrm{99}} {dx} \\ $$
Answered by TANMAY PANACEA last updated on 23/Feb/20
∫sin(n+1)xsin^(n−1) xdx    n=100  ∫(sinnxcosx+cosnxsinx)sin^(n−1) xdx  ∫(sinnxcosxsin^(n−1) x+cosnxsin^n x)dx  ∫(sinnx×((d(sin^n x))/dx)×(1/n)+sin^n x×((d(sinnx))/dx)×(1/n))dx  (1/n)∫(d/dx)(sinnx.sin^n x)dx  (1/n)(sinnx.sin^n x)+c  (1/(100))(sin100xsin^(100) x)+c
$$\int{sin}\left({n}+\mathrm{1}\right){xsin}^{{n}−\mathrm{1}} {xdx}\:\:\:\:{n}=\mathrm{100} \\ $$$$\int\left({sinnxcosx}+{cosnxsinx}\right){sin}^{{n}−\mathrm{1}} {xdx} \\ $$$$\int\left({sinnxcosxsin}^{{n}−\mathrm{1}} {x}+{cosnxsin}^{{n}} {x}\right){dx} \\ $$$$\int\left({sinnx}×\frac{{d}\left({sin}^{{n}} {x}\right)}{{dx}}×\frac{\mathrm{1}}{{n}}+{sin}^{{n}} {x}×\frac{{d}\left({sinnx}\right)}{{dx}}×\frac{\mathrm{1}}{{n}}\right){dx} \\ $$$$\frac{\mathrm{1}}{{n}}\int\frac{{d}}{{dx}}\left({sinnx}.{sin}^{{n}} {x}\right){dx} \\ $$$$\frac{\mathrm{1}}{{n}}\left({sinnx}.{sin}^{{n}} {x}\right)+{c} \\ $$$$\frac{\mathrm{1}}{\mathrm{100}}\left({sin}\mathrm{100}{xsin}^{\mathrm{100}} {x}\right)+{c} \\ $$$$ \\ $$
Commented by peter frank last updated on 23/Feb/20
help qn 74411
$${help}\:{qn}\:\mathrm{74411} \\ $$
Commented by TANMAY PANACEA last updated on 23/Feb/20
ok let me see
$${ok}\:{let}\:{me}\:{see} \\ $$

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