Commerce (English Medium) इयत्ता १२ - CBSE Question Bank Solutions

If `d/dx f(x) = 4x^3 - 3/x^4` such that f(2) = 0, then f(x) is ______.

Integrate the function:

`1/(x - x^3)`

Integrate the function:

`1/(sqrt(x+a) + sqrt(x+b))`

Integrate the function:

`1/(xsqrt(ax - x^2)) ["Hint : Put x" = a/t]`

Integrate the function:

`1/(x^2(x^4 + 1)^(3/4))`

Integrate the function: 

`1/(x^(1/2) + x^(1/3))  ["Hint:" 1/(x^(1/2) + x^(1/3)) = 1/(x^(1/3)(1+x^(1/6))),  "put x" = t^6]`

Integrate the function:

`(5x)/((x+1)(x^2 +9))`

Integrate the function:

`sinx/(sin (x - a))`

Integrate the function:

`(e^(5log x) -  e^(4log x))/(e^(3log x) - e^(2log x))`

Integrate the function:

`cos x/sqrt(4 - sin^2 x)`

Integrate the function:

`(sin^8 x - cos^8 x)/(1-2sin^2 x cos^2 x)`

Integrate the function:

`1/(cos (x+a) cos(x+b))`

Integrate the function:

`x^3/(sqrt(1-x^8)`

Integrate the function:

`e^x/((1+e^x)(2+e^x))`

Integrate the function:

`1/((x^2 + 1)(x^2 + 4))`

Integrate the function:

`cos^3 xe^(log sinx)`

Integrate the function:

`e^(3log x) (x^4 + 1)^(-1)`

Integrate the function:

f' (ax + b) [f (ax + b)]ⁿ

Integrate the function:

`1/sqrt(sin^3 x sin(x + alpha))`

Integrate the functions `(sin^(-1) sqrtx - cos^(-1) sqrtx)/ (sin^(-1) sqrtx + cos^(-1) sqrtx) , x in [0,1]`