\(\int { f(x)dx=g(x)+c } \) எனில், \(\int { f(x){ g }^{ ' }(x)dx } \) என்பது______.

(a)

\(\int { f(x))^{ 2 }dx } \)

(b)

\(\int { f(x)g(x) } \)

(c)

\(\int { { f }^{ ' }(x)g(x) } \)

(d)

\(\int { (g({ x)) }^{ 2 }(x)dx } \)

\(\int { { f }^{ ' }(x){ e }^{ { x }^{ 3 } }dx } =(x-1){ e }^{ { x }^{ 3 } }+c\) எனில், f(x) என்பது ______.

(a)

\(2{ x }^{ 3 }-\frac { { x }^{ 2 } }{ 2 } +x+c\)

(b)

\(\frac { { x }^{ 2 } }{ 2 } +3{ x }^{ 2 }+4x+c\)

(c)

\({ x }^{ 3 }+4{ x }^{ 2 }+6x+c\)

(d)

\(\frac { { 2x }^{ 3 } }{ 3 } -{ x }^{ 2 }+x+c\)

\(\int { e^{ -4x } } \) cos x dx = ______.

(a)

\(\frac { { e }^{ -4x } }{ 17 } \)[4cosx - sinx]+c

(b)

\(\frac { { e }^{ -4x } }{ 17 } \)[-4cosx + sinx] +c

(c)

\(\frac { { e }^{ -4x } }{ 17 } \)[4cosx + sinx] + c

(d)

\(\frac { { e }^{ -4x } }{ 17 } \) [-4cosx - sin x]+c

\(\int { { e }^{ -7x } } \) sin 5xdx = ______.

(a)

\(\frac { { e }^{ -7x } }{ 74 } \) [-7sin 5x - 5cos 5x] + c

(b)

\(\frac { { e }^{ -7x } }{ 74 } \) [7sin 5x + 5 cos 5x]+c

(c)

\(\frac { { e }^{ -7x } }{ 74 } \) [7 sin 5x - 5 cos5x]  + c

(d)

\(\frac { { e }^{ -7x } }{ 74 } \) [-7 sin 5x + 5 cos 5x] + c

\(\int { \frac { { \sin }^{ 8 }x-{ \cos }^{ 8 }x }{ 1-2{ \sin }^{ 2 }x{ \cos }^{ 2 }x } dx= } \)______.

(a)

\(\frac { 1 }{ 2 } \sin2x+c\)

(b)

\(-\frac { 1 }{ 2 } \sin2x+c\)

(c)

\(\frac { 1 }{ 2 } \cos2x+c\)

(d)

\(-\frac { 1 }{ 2 } \cos2x+c\)