The value of ∫ ( cos 3 x/ sin 2 x+ sin x) d x is equal to:

Question

Tardigrade Admin · Accepted Answer

I=∫ ( cos 3 x/ sin 2 x+ sin x) d x=∫ ( cos x ⋅(1- sin 2 x)/ sin x(1+ sin x)) d x Put sin x=t, then cos x d x=d t ⇒ I=∫ ((1-t)(1+t) d t/t(1+t)) =ℓ n|t|-t+C=ℓ n| sin x|- sin x+C

Q. The value of $\int \frac{c o s ^{3} x}{s i n ^{2} x + s i n x} d x$ is equal to:

$ℓ n ∣ sin x ∣ + sin x + C$

$ln ∣ sin x ∣ - sin x + C$

$- ℓ n ∣ sin x ∣ - sin x + C$

$- ℓ n ∣ sin x ∣ + sin x + C$

Q. The value of ∫sin2x+sinxcos3x​dx is equal to:

ℓn∣sinx∣+sinx+C

ln∣sinx∣−sinx+C

−ℓn∣sinx∣−sinx+C

−ℓn∣sinx∣+sinx+C

I=∫sin2x+sinxcos3x​dx=∫sinx(1+sinx)cosx⋅(1−sin2x)​dx Put sinx=t, then cosxdx=dt ⇒I=∫t(1+t)(1−t)(1+t)dt​ =ℓn∣t∣−t+C=ℓn∣sinx∣−sinx+C

Q. The value of $\int \frac{c o s ^{3} x}{s i n ^{2} x + s i n x} d x$ is equal to:

$ℓ n ∣ sin x ∣ + sin x + C$

$ln ∣ sin x ∣ - sin x + C$

$- ℓ n ∣ sin x ∣ - sin x + C$

$- ℓ n ∣ sin x ∣ + sin x + C$