then y y_{1} (where y_{1} = dy/dx) is equal to
The derivative of (x^{2}–1)/x is
The differential coefficients of (x^{2} +1)/x is
If y = then is equal to _____.
If x = (1 – t^{2} )/(1 + t^{2}) y = 2t/(1 + t^{2}) then dy/dx at t =1 is _____________.
f(x) = x^{2}/e^{x} then f ’(1) is equal to _____________.
Evaluate ∫ 5x^{2} dx and the answer will be
Integration of 3 – 2x – x^{4} will become
Given f(x) = 4x^{3} + 3x^{2} – 2x + 5, ∫ f(x) dx is
Evaluate ∫ () dx . The value is
∫ (1  3x) (1 + x) dx is equal to
The integral of px^{3} + qx^{2} + rk + w/x is equal to
Use method of substitution to integrate the function f(x) = (4x + 5)^{6} and the answer is
Use method of substitution to evaluate ∫ x (x^{2} + 4)^{5}dx and the answer is
Integrate (x + a)^{n }and the result will be
∫ 8x^{2}/ (x^{3} + 2)^{3} dx is equal to
Using method of partial fraction find the integration of f(x) when f(x) = 1/x^{2} – a^{2} and the answer is
Use integration by parts to evaluate ∫ x^{2} e^{3x }dx and the answer is
∫ logx dx is equal to
∫ x e^{x} dx is
∫ (logx)^{2} dx and the result is
Using method of partial fraction to evaluate ∫ (x + 5) dx/(x + 1) (x + 2)^{2} and the final answer becomes
Let x
x = t. Then,d(x^{x}) = dt
d(e^{xlogx}) = dt
e^{xlogx} (logx+1)dx = dt
x^{x}(1+logx)dx=dt
Therefore, I = ∫x^{x}(1+logx) dx
I= ∫dt = t+C = x^{x }+ C
then ∫ f(x)dx is
∫ (e^{x} – e^{–x})2 (e^{x} – e^{–x}) dx is
^{a}∫_{0} [ f(x) + f(–x) ] dx is equal to
∫ xe^{x}/(x + 1)^{2} dx is equal to
∫ (x^{4} + 3/x ) dx is equal to
Evaluate the integral ∫ (1 − x)^{3}/ x dx and the answer is equal to
The equation of the curve in the form y = f(x) if the curve passes through the point (1, 0) and f’(x) = 2x – 1 is
Evaluate dx and the value is
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