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Mathematics
\[\int\frac{2}{\left( e^x + e^{- x} \right)^2} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{e^x \left( 1 + x \right)}{\cos^2 \left( x e^x \right)} dx =\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
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\[\int\frac{\sin^2 x}{\cos^4 x} dx =\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
The primitive of the function \[f\left( x \right) = \left( 1 - \frac{1}{x^2} \right) a^{x + \frac{1}{x}} , a > 0\text{ is}\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\sqrt{\frac{x}{1 - x}} dx\] is equal to
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int e^x \left\{ f\left( x \right) + f'\left( x \right) \right\} dx =\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
The value of \[\int\frac{\sin x + \cos x}{\sqrt{1 - \sin 2x}} dx\] is equal to
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{\cos 2x - 1}{\cos 2x + 1} dx =\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{\cos2x - \cos2\theta}{\cos x - \cos\theta}dx\] is equal to
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{x^9}{\left( 4 x^2 + 1 \right)^6}dx\] is equal to
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{x^3}{\sqrt{1 + x^2}}dx = a \left( 1 + x^2 \right)^\frac{3}{2} + b\sqrt{1 + x^2} + C\], then
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{x^3}{x + 1}dx\] is equal to
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
If \[\int\frac{1}{\left( x + 2 \right)\left( x^2 + 1 \right)}dx = a\log\left| 1 + x^2 \right| + b \tan^{- 1} x + \frac{1}{5}\log\left| x + 2 \right| + C,\] then
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{1}{\sqrt{x} + \sqrt{x + 1}} \text{ dx }\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{1 - x^4}{1 - x} \text{ dx }\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{x + 2}{\left( x + 1 \right)^3} \text{ dx }\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{\left( 2^x + 3^x \right)^2}{6^x} \text{ dx }\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{\sin x}{1 + \sin x} \text{ dx }\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{x^4 + x^2 - 1}{x^2 + 1} \text{ dx}\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int \sec^2 x \cos^2 2x \text{ dx }\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
