Evaluate - tannxsec2x

∫tan ^ n x . ^ 2 x #160; dx Let tanx=t ^ 2 x #160; dx=dt I=∫tan ^ n x . ^ 2 x #160; dx I=∫ t ^ n .dt = t ^ n+1 n+1 ...

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Byju's Answer

Standard XII

Mathematics

Implicit Differentiation

Evaluate ∫ ...

Question

Evaluate $\int t a n^{n} x s e c^{2} x$

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Solution

$\int {tan}^{n} x . {sec}^{2} x d x$
Let $tan x = t$
${sec}^{2} x d x = d t$
$I = \int {tan}^{n} x . {sec}^{2} x d x$
$I = \int t^{n} . d t = \frac{t^{n + 1}}{n + 1} + C = \frac{1}{n + 1} . + C$

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Evaluate ∫tannxsec2x

∫tannx.sec2xdxLet tanx=tsec2xdx=dtI=∫tannx.sec2xdxI=∫tn.dt=tn+1n+1+C=1n+1.+C

Evaluate $\int t a n^{n} x s e c^{2} x$

$\int {tan}^{n} x . {sec}^{2} x d x$
Let $tan x = t$
${sec}^{2} x d x = d t$
$I = \int {tan}^{n} x . {sec}^{2} x d x$
$I = \int t^{n} . d t = \frac{t^{n + 1}}{n + 1} + C = \frac{1}{n + 1} . + C$