The value of the integral \int{\sin\\theta \sin\2\\theta(\sin ^{6} \theta+\sin ^{4} \theta+\sin ^{2} \theta) \sqrt{2 \sin ^{4} \theta+3 \sin ^{2} \theta+6}}/{ 1-\cos2\theta}\d\theta is (where, c is a constant of integration) [25 Feb 2021 Shift 1]

Correct Answer is : 118[11−18cos2θ+9cos4θ−2cos6θ]32+c

\frac{1}{18}[11-18 \sin ^{2} \theta+9 \sin ^{4} \theta-2 \sin ^{6} \theta]^{\frac{3}{2}}+c

\frac{1}{18}[9-2 \cos ^{6} \theta- 3 \cos ^{4} \theta-6 \cos ^{2} \theta]^{\frac{3}{2}}+c

\frac{1}{18}[9-2 \sin ^{6} \theta-3 \sin ^{4} \theta-6 \sin ^{2} \theta]^{\frac{3}{2}}+c

\frac{1}{18}[11-18 \cos ^{2} \theta+9 \cos ^{4} \theta-2 \cos ^{6} \theta]^{\frac{3}{2}}+c

Indefinite Integrals

Section: Mathematics

Question : 44 of 89

Marks: +1, -0

The value of the integral

∫

sin‌θ‌sin‌2‌θ(sin6θ+sin4θ+sin2θ)‌√2sin4θ+3sin2θ+6

1−cos‌2‌θ

dθ

is (where, c is a constant of integration)

[25 Feb 2021 Shift 1]

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