Write a value of ∫ tanx sec3x dx.

1.	Write a value of ∫ tanx sec3x dx.
Answer» Given, ∫ tanx sec³x dx = ∫ (tanx secx) sec²x dx Let secx = t Differentiating on both sides we get, tanx secx dx = dt Substituting above equation in ∫ tanx sec³x dx we get, = ∫t² dt = \(\frac{t^3}{3}+c\) = \(\frac{sec^3x}{3}\) + c

Answer»

Given,

∫ tanx sec³x dx

= ∫ (tanx secx) sec²x dx

Let secx = t

Differentiating on both sides we get,

tanx secx dx = dt

Substituting above equation in ∫ tanx sec³x dx we get,

= ∫t² dt

= \(\frac{t^3}{3}+c\)

= \(\frac{sec^3x}{3}\) + c

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