If In - m - -sinnx-cosmx dx then In - m - n - 1-m - 1 In - 2- 2 - m is equal to -

The correct option is B 1/(m 1) sin^n 1x/cos^m 1x I_n m = sin^n 1x/(m 1) cos^m 1x n 1/m 1 ∫sin^n 2x/cos^ ...

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Special Integrals - 1

If In - m =...

Question

If $I_{n - m} = \int \frac{s i n^{n} x}{c o s^{m} x} d x$ then $I_{n - m} + \frac{n -, 1}{m - 1} I_{n - 2, 2 - m}$ is equal to -

\frac{s i n^{n - 1} x}{c o s^{m - 1} x}

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\frac{1}{(m - 1)} \frac{s i n^{n - 1} x}{c o s^{m - 1} x}

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\frac{1}{(n - 1)} \frac{s i n^{n - 1} x}{c o s^{m - 1} x}

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\frac{n - 1}{(m - 1)} \frac{s i n^{n - 1} x}{c o s^{m - 1} x}

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f (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} ω^{3} & ω^{4} & ω^{5} sin (m - 1) x & sin m x & sin (m + 1) x cos (m - 1) x & cos m x & cos (m + 1) x \end{matrix} ∣ ∣ ∣ ∣ ∣

m \in N

ω

π / 2 \int 0 f (x) d x = a ω + b ω^{2},

(a, b) =

n

\int \frac{{cos}^{m} x}{{sin}^{n} x} d x = \frac{{cos}^{m - 1} x}{(m - n) {sin}^{n - 1} x} + A \int \frac{{cos}^{m - 2} x}{{sin}^{n} x} d x + C

A

$\int \frac{c o s^{n - 1} x}{s i n^{n + 1} x} d x, n \neq 0$ is

{log}_{m + 1} (x + \sqrt{m + 1} y) + {log}_{m + 1} (x - \sqrt{m + 1} y) = 1

m > 0

(m - n) x^{2} + (n - 1) x + 1 - m = 0

1

m

n

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