Displaystyle int-frac-cosx-x-sin-x-log x-dx-log x- -cos x- -c -log x- sinx-c2-log x- -cos x- -c-log x- sin x-c

Question

Toppr Admin · Accepted Answer

-x222B-cos-xA0-xx-x2212-sinx-xA0-log-xA0-x-dx-x222B-cos-xA0-xxdx-x2212-xA0-x222B-xA0-sin-xA0-x-xA0-log-xA0-x-xA0-dxcos-xA0-x-xA0-x222B-1x-xA0-dx-xA0-x222B-xA0-sin-xA0-x-xA0-log-xA0-x-xA0-dx -x2212-x222B-xA0-sin-xA0-x-xA0-log-xA0-x-xA0-dx-xA0-cos-xA0-x-log-xA0-x-cHence- -x222B-cosxx-x2212-sin-xA0-x-log-xA0-x-dx-xA0-cos-xA0-x-xA0-log-xA0-x-c

INTEGRAND	INTEGRAL
$\int x^{n} d x$	$\frac{x^{n}}{n + 1} + C$
$\int \frac{1}{x} d x$	$ln (x \| + C$
$\int e^{x} d x$	$e^{x} + C$
$\int a^{x} d x$	$\frac{a^{x}}{ln a} + C$
$\int cos x d x$	$sin x + C$
$\int sin x d x$	$cos x + C$
$\int sec x tan x d x$	$sec x + C$
$\int cosec x cot x d x$	$- cosec x + C$
$\int {sec}^{2} x d x$	$tan x + C$
$\int {cosec}^{2} x d x$	$cot x + C$

∫[cosxx−sinxlogx]dx=(logx)(cosx)+c(logx)sinx+c2(logx)(cosx)+c−(logx)sinx+c

∫[cos xx−sinx log x]dx∫cos xxdx− ∫ sin x log x dxcos x ∫1x dx+ ∫ sin x log x. dx −∫ sin x log x dx.=( cos x)(log x)+cHence, ∫[cosxx−(sin x)(log x)]dx=( cos x)( log x)+c

$\int [\frac{c o s x}{x} - sin x log x] d x =$
$(log x) (c o s x) + c$
$(log x) s i n x + c$
$2 (log x) (c o s x) + c$
$- (log x) s i n x + c$