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Mathematics
\[\int\frac{x}{\left( x^2 + 4 \right) \sqrt{x^2 + 9}} \text{ dx}\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
Write a value of
\[\int e^{3 \text{ log x}} x^4\text{ dx}\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
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Write the anti-derivative of \[\left( 3\sqrt{x} + \frac{1}{\sqrt{x}} \right) .\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{x}{4 + x^4} \text{ dx }\] is equal to
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{1}{\cos x + \sqrt{3} \sin x} \text{ dx } \] is equal to
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
` \int \text{ x} \text{ sec x}^2 \text{ dx is equal to }`
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
If \[\int\frac{1}{5 + 4 \sin x} dx = A \tan^{- 1} \left( B \tan\frac{x}{2} + \frac{4}{3} \right) + C,\] then
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int x^{\sin x} \left( \frac{\sin x}{x} + \cos x . \log x \right) dx\] is equal to
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
If \[\int\frac{\cos 8x + 1}{\tan 2x - \cot 2x} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
If \[\int\frac{\sin^8 x - \cos^8 x}{1 - 2 \sin^2 x \cos^2 x} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\left( x - 1 \right) e^{- x} dx\] is equal to
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
If `int(2x^(1/2))/(x^2) dx = k . 2^(1/x) + C`, then k is equal to ______.
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{1}{1 + \tan x} dx =\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int e^x \left( 1 - \cot x + \cot^2 x \right) dx =\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{\sin^6 x}{\cos^8 x} dx =\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
If P, Q and R are three collinear points such that \[\overrightarrow{PQ} = \vec{a}\] and \[\overrightarrow{QR} = \vec{b}\]. Find the vector \[\overrightarrow{PR}\].
Chapter: [10] Vectors
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{1}{7 + 5 \cos x} dx =\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{1}{1 - \cos x - \sin x} dx =\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{\sin x}{3 + 4 \cos^2 x} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int e^x \left( \frac{1 - \sin x}{1 - \cos x} \right) dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
