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For given vectors, `veca = 2hati - hatj + 2hatk` and `vecb = -hati + hatj - hatk`, find the unit vector in the direction of the vector `veca +vecb`.
Concept: undefined >> undefined
Find a vector in the direction of vector `5hati - hatj +2hatk` which has a magnitude of 8 units.
Concept: undefined >> undefined
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Show that the direction cosines of a vector equally inclined to the axes OX, OY, and OZ are `pm1/sqrt3, 1/sqrt3, 1/sqrt3`.
Concept: undefined >> undefined
Integrate the rational function:
`x/((x + 1)(x+ 2))`
Concept: undefined >> undefined
Integrate the rational function:
`1/(x^2 - 9)`
Concept: undefined >> undefined
Integrate the rational function:
`(3x - 1)/((x - 1)(x - 2)(x - 3))`
Concept: undefined >> undefined
Integrate the rational function:
`x/((x-1)(x- 2)(x - 3))`
Concept: undefined >> undefined
Integrate the rational function:
`(2x)/(x^2 + 3x + 2)`
Concept: undefined >> undefined
Integrate the rational function:
`(1 - x^2)/(x(1-2x))`
Concept: undefined >> undefined
Integrate the rational function:
`x/((x^2+1)(x - 1))`
Concept: undefined >> undefined
Integrate the rational function:
`x/((x -1)^2 (x+ 2))`
Concept: undefined >> undefined
Integrate the rational function:
`(3x + 5)/(x^3 - x^2 - x + 1)`
Concept: undefined >> undefined
Integrate the rational function:
`(2x - 3)/((x^2 -1)(2x + 3))`
Concept: undefined >> undefined
Integrate the rational function:
`(5x)/((x + 1)(x^2 - 4))`
Concept: undefined >> undefined
Integrate the rational function:
`(x^3 + x + 1)/(x^2 -1)`
Concept: undefined >> undefined
Integrate the rational function:
`2/((1-x)(1+x^2))`
Concept: undefined >> undefined
Integrate the rational function:
`(3x -1)/(x + 2)^2`
Concept: undefined >> undefined
Integrate the rational function:
`1/(x^4 - 1)`
Concept: undefined >> undefined
Integrate the rational function:
`1/(x(x^n + 1))` [Hint: multiply numerator and denominator by xn − 1 and put xn = t]
Concept: undefined >> undefined
Integrate the rational function:
`(cos x)/((1-sinx)(2 - sin x))` [Hint: Put sin x = t]
Concept: undefined >> undefined
