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Mathematics
Express the following matrix as the sum of a symmetric and skew-symmetric matrix and verify your result:
\[\begin{bmatrix}3 & - 2 & - 4 \\ 3 & - 2 & - 5 \\ - 1 & 1 & 2\end{bmatrix}\]
Chapter: [3] Matrices
Concept: undefined >> undefined
Concept: undefined >> undefined
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\[\int\frac{x - 1}{\sqrt{x + 4}} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{x}{\sqrt{x + 4}} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\sqrt{\frac{1 - \cos x}{1 + \cos x}} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
Evaluate the following integrals:
`int "sec x"/"sec 2x" "dx"`
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{\cos 2x}{\left( \cos x + \sin x \right)^2} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{1 + \tan x}{1 - \tan x} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{e^{2x}}{e^{2x} - 2} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{2 \cos x - 3 \sin x}{6 \cos x + 4 \sin x} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{\cos 2x + x + 1}{x^2 + \sin 2x + 2x} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{1}{\cos\left( x + a \right) \cos\left( x + b \right)}dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{sec x}{\log \left( \text{sec x }+ \text{tan x} \right)} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{{cosec}^2 x}{1 + \cot x} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{10 x^9 + {10}^x \log_e 10}{{10}^x + x^{10}} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
` ∫ {1+tan}/{ x + log sec x dx} `
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{1}{\sqrt{x}\left( \sqrt{x} + 1 \right)} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
