Calculate \int_{-4\pi}^{4\pi} \frac{(\sin x)^2-(\sin x)^4}{1-(\sin x)^4}dx

ardeinduie

ardeinduie

Answered question

2022-01-26

Calculate 4π4π(sinx)2(sinx)41(sinx)4dx

Answer & Explanation

votaren10

votaren10

Beginner2022-01-27Added 11 answers

Doing x=arctant and dx=11+t2dt, you get
sin2x1+sin2xdx
=t22t4+3t2+1dt
=1t2+112t2+1dt
Larissa Hogan

Larissa Hogan

Beginner2022-01-28Added 10 answers

Hint:
(sinx)2(sinx)41(sinx)4=
=11sin2x1(sinx)4=
=111+sin2x=
=1sec2x1+2tan2x

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