Tangent at `(1,e)` on the curve `y=x\ e^(x^2)`, also passes through the point (a) `((4)/(3),2e)` (b) `((5)/(3),e)` (c) `((4)/(3),3e)` (d) `((3)/(4),3e)`

Tangent at (1,e) on the curve y=x backslash e^(x^(2)), also passes through the point (a) ((4)/(3),2e) (b) ((5)/(3),e)(c)((4)/(3),3e) (d) ((3)/(4),3e)

The tangent to the curve y=xe^(x^2) passing through the point (1,e) also passes through the point

When the tangent to the curve y=xlogx is parallel to the chord joining the points (1, 0) and (e ,\ e) , the value of x is e^(1//1-e) (b) e^((e-1)(2e-1)) (c) e^((2e-1)/(e-1)) (d) (e-1)/e

int (2e ^ (5x) + e ^ (4x) -4e ^ (3x) + 4e ^ (2x) + 2e ^ (x)) / (e ((2x) +4) (e ^ (2x) - 1) ^ (2)) dx

y = e ^ (2x) + e ^ (3x)

int x^2 . e^(x^3) dx = (a) e^(x^3) + C (b) e^(x^2) + C (c) 1/3 e^(x^3) + C (d) 1/3 e^(x^2) + C

int (e ^ (3x) + e ^ (x)) / (e ^ (4x) -e ^ (2x) +1) dx

[[log e, log e ^ (2), log e ^ (3) log e ^ (2), log e ^ (3), log e ^ (4) log e ^ (3), log e ^ (4) ), log e ^ (5)]]

(1) / (log_ (3) e) + (1) / (log_ (3) e ^ (2)) + (1) / (log_ (3) e ^ (4)) + ... =