The integral I=∫ (1/x ⋅ sec x)- ln x sin x d x simplifies to (where, c is the constant of integration)

Question

The integral I=∫ (1/x ⋅ sec x)- ln x sin x d x simplifies to (where, c is the constant of integration) (A)  ln x sin x+c (B)  ln x cos x+c (C) x ln sin x+c (D) x ln cos x+c

Tardigrade Admin · Accepted Answer

Given I=∫ cos x ⋅ (1/x)+- sin x ln x d x Since, ∫ f ⋅ g prime+f prime g d x =f ⋅ g+c ⇒ I= cos x ln x+c

Q. The integral $I = \int \frac{1}{x \cdot s e c x} - ln x^{s i n x} d x$ simplifies to (where, $c$ is the constant of integration)

$ln x sin x + c$

$ln x cos x + c$

$x ln sin x + c$

$x ln cos x + c$

Given $I = \int cos x \cdot \frac{1}{x} + - sin x ln x d x$ Since, $\int f \cdot g^{'} + f^{'} g d x$
$= f \cdot g + c$
$\Rightarrow I = cos x ln x + c$

Q. The integral I=∫x⋅secx1​−lnxsinxdx simplifies to (where, c is the constant of integration)

lnxsinx+c

lnxcosx+c

xlnsinx+c

xlncosx+c