Question

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\begin{gathered} \bf {Let \: I_n = \int { tan}^{n} \: x \: dx(n > 1)} \\ \\ \bf If \: I_4 + I_6 = a. {tan}^{5}x + b {x}^{5} + C\end{gathered}LetIn​=∫tannxdx(n>1)IfI4​+I6​=a.tan5x+bx5+C​
Then Find Values of a & b
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Answer 1

$\huge{❥}\:{\mathtt{{\purple{\boxed{\tt{\pink{\red{A}\pink{n}\orange{s}\green{w}\blue{e}\purple{r᭄}}}}}}}}❥$

We have,

$ln = \int { \tan }^{n} \times dx \\ \: ln + ln + 2 = \int { \tan}^{n} \times dx + \int { \tan}^{n} { + }^{2} \times dx \\ = \int { \tan }^{n} \times (1 + { \tan}^{2} x)dx \\ = \int { \tan}^{n} \times { \sec}^{2} \times dx = \frac{{ \tan}^{n} { + }^{2} }{n + 1} + c \\ put \: n = 4 \: we \: get \: l4 + l6 = \frac{ { \tan }^{2} x }{5} + c \\ a = \frac{1}{5} \: and \: b = 0$

Hence,this is the required answer.