No links please: Q Integrate : ∫1+cosecx dx - Maths - Integrals

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Q Integrate : ∫ 1 + cos e c x   d x

Lovina Kansal · Accepted Answer

Dear student
Let I=∫1+cosecxdx=∫1sinx+1dx=∫1+sinxsinxdx=∫1+sinxsinx×1-sinx1-sinxdx=∫1-sin2xsinx(1-sinx)dx=∫cos2xsinx1-sinxdx=∫cosxsinx(1-sinx)dxTake u=sinx⇒dx=2sinxcosxduSo,I=2∫du1-u2=2sin-1u+C=2sin-1sinx+C
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No links please: Q. Integrate : ∫ 1 + cos e c x d x

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Q. Integrate : $\int \sqrt{1 + \cos e c x} d x$