Indefinite Integrals
Showing 50 of 416 · 416 total
- 1.Let f(x)= (16x+24x^2+2x-15)dx.Medium
- 2.Let [ f(x)= d xx^2 / 3+2 x^1 / 2, ] be such that f(0) = -26 + 24 _e(2).Medium
- 3.If (1-5 ^2x ^5x ^2x)dx=f(x)+C, where C is the constant of integration, then f(( )/(6))-f((…Medium
- 4.Let f(t)= (1- ( _et)1- ( _et))dt,t>1.Medium
- 5.Let I(x)= 3dx(4x+6)(√4x^2+8x+3) and I(0)=√34+20.Hard
- 6.Let f(x)= (2-x^2) e^x(√1+x)(1-x)^3/2dx.Hard
- 7.f(x)= x^3√3-x^2dx5f(√2)=-4f(1)Medium
- 8.If f(x)= 1x^1/4(1+x^1/4)dx,f(0)=-6, then f(1) is equal to :Medium
- 9.Let x^3 xdx=g(x)+C, where C is the constant of integration.Medium
- 10.Let I(x)= dx(x-11)^(11)/(13)(x+15)^(15)/(13).Medium
- 11.If e^x(x ^-1x√1-x^2+ ^-1x(1-x^2)^3/2+x1-x^2)dx=g(x)+C, where C is the constant of integrat…Medium
- 12.Let (2- x)/(3+ x)dx=(1)/(2)( x+ _e| x+ x|)+C, where C is the constant of integration.Medium
- 13.Let I(x)= 6 ^2x(1- x)^2dx.Medium
- 14.If 1a^2 ^2x+b^2 ^2xdx=(1)/(12) ^-1(3 x)+ constant, then the maximum value of a x+b x, is :Medium
- 15.If ^(3)/(2)x+ ^(3)/(2)x ^3x ^3x (x- )dx=A x- +B - x+C, where C is the integration constant…Hard
- 16.For x (-( )/(2),( )/(2)), if y(x)= x+ x x x+ x ^2xdx, and x (( )/(2))^-limy(x)=0 then y(( …Medium
- 17.(x^8-x^2)dx(x^12+3x^6+1) ^-1(x^3+1x^3)Medium
- 18.For , , , N, if (((x)/(e))^2x+((e)/(x))^2x) _exdx=(1)/( )((x)/(e))^ x-(1)/( )((e)/(x))^ x+…Medium
- 19.If I(x)= e^ ^2x( x 2x- x)dx and I(0)=1, then I(( )/(3)) is equal to :Medium
- 20.The integral [((x)/(2))^x+((2)/(x))^x] ((ex)/(2))dx is equal to :Medium
- 21.Let I(x)= (x+1)x(1+xe^x)^2dx,x>0.Medium
- 22.Let I(x)= x^2(x ^2x+ x)(x x+1)^2dx.Hard
- 23.If ( x)^(-11)/(2)( x)^(-5)/(2) d x= -(p_1)/(q_1)( x)^(9)/(2)-(p_2)/(q_2)( x)^(5)/(2)-(p_3)…Hard
- 24.If ((1)/(x)+1x^3)(√233x^-24+x^-26)dx=-( )/(3( +1))(3x^ +x^ )^( +1)/( )+C,x>0,( , , Z), whe…Medium
- 25.If (√1+x^2+x)^10(√1+x^2-x)^9dx=(1)/(m)((√1+x^2+x)^n(n√1+x^2-x))+C where C is the constant …Hard
- 26.If 2x^2+5x+9x^2+x+1dx=xx^2+x+1+ x^2+x+1+ _e|x+(1)/(2)+x^2+x+1|+C, where C is the constant …Medium
- 27.If 1√5(x-1)^4(x+3)^6dx=A(( x-1)/( x+3))^B+C, where C is the constant of integration, then …Medium
- 28.If ^5xdx= x x( ^2x+(3)/(2))+ _x| (x)/(2)|+C where , R and C is the constant of integration…Hard
- 29.Let f(x)= dx(3+4x^2)√4-3x^2,|x|0, then ^2+ ^2 is equal to ____________.Hard
- 30.Let I(x)= (x+7)/(x)dx and I(9)=12+7 _e7.Medium
- 31.If 2x-1dx= _e| 2x+ + 2x(1+ (1)/( )x)|+ constant, then - is equal to ____________.Hard
- 32._0^1 4^-1(1-2x+4x^2),dx = a^-1(2) - b_e(5), where a,bN.Hard
- 33.Let [] be the greatest integer function.Medium
- 34.The value of _r=1^20(_0^r x,| x|,dx) is ____.Medium
- 35.If = 2√3_0^2√3_2(x^2+4),dx + _2^4√2x-4,dx, then ^2 is equal to ________.Medium
- 36.The value of _-/6^/6(+4x)/(1-(|x|+/6)),dx is equal to:Medium
- 37.Let f:[1,)R be differentiable.Medium
- 38.Let f be a polynomial function such that f(x^2+1) = x^4+5x^2+2, for all xR.Medium
- 39.The value of _0^3e^x+e^-x[x]!,dx, where [] is the greatest integer function, is equal to:Medium
- 40.I_1+I_2 where _-2^2(| x|+[x x])dx = 2(3- 2)+ ([] greatest integer function).Hard
- 41.If =1 and =1+i√2 (i=-1), where , are two roots of the equation x^3+ax^2+bx+c=0 (a,b,cR), t…Medium
- 42.The value of the integral _ 2^ 3e^2xe^4x-1,dx is equal to:Medium
- 43._-1^1((x^3+|x|+1)/(x^2+2|x|+1))dx is equal to:Medium
- 44.Let f(x) = cases13, & x /2[4pt] b(1- x)(-2x)^2, & x>/2cases.Medium
- 45.If ( x)^-11/2( x)^-5/2,dx = -p_1q_1( x)^9/2 - p_2q_2( x)^5/2 - p_3q_3( x)^1/2 + p_4q_4( x)…Hard
- 46.Let f(x) = (2-x^2)e^x√1+x,(1-x)^3/2,dx, with f(0)=0.Medium
- 47.Let I(x) = 3,dx(4x+6)√4x^2+8x+3.Medium
- 48.If ((1-5^2x)/(^5x^2x))dx = f(x)+C, where C is the constant of integration, then f(6)-f(4) …Medium
- 49.Let f(x) = dxx^2/3+2x^1/2.Medium
- 50.Let f:(0,)R be a twice differentiable function.Medium