Integration by Substitution
Trending Questions
Q. ∫cosx+xsinxx(x+cosx)dx=
- −log|xx+cosx|+c
- log|x+cosx2x|+c
- −log|x+cosx2x|+c
- log|xx+cosx|+c
Q. If ∫(x−1x+1)dx√x3+x2+x=2tan−1√f(x)+C, find f(x).
- x+1x+1
- x+1x+2
- x−1x+1
- x−1x−1
Q. ∫(x−x5)1/5x6dx is equal to
- 524(1x4−1)6/5+C
- 524(1−1x4)6/5+C
- −524(1x4−1)6/5+C
- None of these
Q. ∫dxx12(1+x2)5/4 is equal to
- 2√x4√√1+x2+C
- −√x4√√1+x2+C
- √x4√√1+x2+C
- −2√x4√√1+x2+C
Q. ∫(x+1)x(1+xex)2dx is equal to
- log(x1+xex)+11+xex+C
- None of these
- log(1+xexxex)+11+xex+C
- log(xex1+xex)+11+exx+C
Q. Let S(x)=∫dxex+8e−x+4e−3x, R(x)=∫dxe3x+8ex+4e−x and M(x)=S(x)−2R(x). If M(x)=12tan−1(f(x))+c then f(0)=
- 32
- 12
- 52
- 72
Q. ∫x3(1+x2)1/3dx is equal to
- 203(1+x2)23(2x2−3)+C
- 320(1+x2)23(2x2+3)+C
- None of these
- 320(1+x2)23(2x2−3)+C
Q. ∫x.(xx)x.(2 log x+1)dx is equal to
- x(xx)+C
- (xx)x+C
- xx.log x+C
- None of these
Q. ∫√5+x10x16dx=
- −175(1+5x10)+c
- −175(1+5x10)3/2+c
- −150(1+5x10)3/2+c
- −175(1+5x10)5/2+c
Q. ∫[f(x)g′(x)+g(x)f′(x)]f(x).g(x)[log f(x)+log g(x)] dx is equal to
- f(x)g(x) log(f(x)g(x)+C
- 12[logf(x)g(x)]2+C
- [logf(x)g(x)]2+C
- log f(x).g(x)+C