Evaluate ∫cos2(x)tan3(x)dx using trigonometric substitution

Krzychau1

Krzychau1

Answered

2022-01-14

Evaluate cos2(x)tan3(x)dx using trigonometric substitution

Answer & Explanation

Vivian Soares

Vivian Soares

Expert

2022-01-15Added 36 answers

cos2xtan3xdx=sin3xcosxdx=(1cos2x)sinxcosxdx
Let cosx=tsinxdx=dt
=(t21)dtt
=(t1t)dt
sonorous9n

sonorous9n

Expert

2022-01-16Added 34 answers

Use the definition of tanx, then after a bit of algebra you have
sinxcosxcosxsinx
The first one is solved using logarithm subsitution, the second using the identity 2sinxcosx=sin2x

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