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Mathematics
\[\int \sin^{- 1} \left( 3x - 4 x^3 \right) \text{ dx}\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int \left( \sin^{- 1} x \right)^3 dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
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\[\int \cos^{- 1} \left( 1 - 2 x^2 \right) \text{ dx }\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{x \sin^{- 1} x}{\left( 1 - x^2 \right)^{3/2}} \text{ dx}\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int e^{2x} \left( \frac{1 + \sin 2x}{1 + \cos 2x} \right) dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int e^x \frac{\left( 1 - x \right)^2}{\left( 1 + x^2 \right)^2} \text{ dx }\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{\sqrt{1 - \sin x}}{1 + \cos x} e^{- x/2} \text{ dx}\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{e^{m \tan^{- 1} x}}{\left( 1 + x^2 \right)^{3/2}} \text{ dx}\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{x^2}{\left( x - 1 \right)^3 \left( x + 1 \right)} \text{ dx}\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{x}{x^3 - 1} \text{ dx}\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{1}{1 + x + x^2 + x^3} \text{ dx }\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{1}{\left( x^2 + 2 \right) \left( x^2 + 5 \right)} \text{ dx}\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{x^2 - 2}{x^5 - x} \text{ dx}\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\sqrt{\frac{1 - \sqrt{x}}{1 + \sqrt{x}}} \text{ dx}\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{x^2 + x + 1}{\left( x + 1 \right)^2 \left( x + 2 \right)} \text{ dx}\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{\sin 4x - 2}{1 - \cos 4x} e^{2x} \text{ dx}\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{\cot x + \cot^3 x}{1 + \cot^3 x} \text{ dx}\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
If \[\vec{a}\], \[\vec{b}\], \[\vec{c}\] are non-coplanar vectors, prove that the points having the following position vectors are collinear: \[\vec{a,} \vec{b,} 3 \vec{a} - 2 \vec{b}\]
Chapter: [10] Vectors
Concept: undefined >> undefined
Concept: undefined >> undefined
If \[\vec{a}\], \[\vec{b}\], \[\vec{c}\] are non-coplanar vectors, prove that the points having the following position vectors are collinear: \[\vec{a} + \vec{b} + \vec{c} , 4 \vec{a} + 3 \vec{b} , 10 \vec{a} + 7 \vec{b} - 2 \vec{c}\]
Chapter: [10] Vectors
Concept: undefined >> undefined
Concept: undefined >> undefined
Using vectors, find the value of λ such that the points (λ, −10, 3), (1, −1, 3) and (3, 5, 3) are collinear.
Chapter: [10] Vectors
Concept: undefined >> undefined
Concept: undefined >> undefined
