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$\int \sin^{3} {xcos}^{3} xdx$ is equal to

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sin6⁡x6−cos4⁡x4+C

sin6⁡x3−cos4⁡x2+C

cos6⁡x6−cos4⁡x4+C

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detailed solution

Correct option is C

∫sin3⁡x⋅cos3⁡xdxLet cos⁡x=t⇒−sin⁡x=dtdx⇒dx=−dtsin⁡x∴∫sin3⁡x⋅cos3⁡xdx=∫sin3⁡x⋅t3dt−sin⁡x =−∫sin2⁡x⋅t3dt=−∫t31−cos2⁡xdt =−∫t31−t2dt=−∫t3−t5dt =−t44−t66+C=cos6⁡x6−cos4⁡x4+C

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∫sin3⁡xcos3⁡xdx is equal to

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$\int \sin^{3} {xcos}^{3} xdx$ is equal to