Evaluate -cos 3 x e log sin x dx

∫cos^3xe^log(sinx)dx =∫cos^3xsinxdx Let t=cosx⇒ dt= sinxdx = ∫t^3dt = t^44+c = cos^4x4+c ...

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Byju's Answer

Standard XII

Mathematics

Integration by Parts

Evaluate ∫c...

Question

Evaluate $\int {cos}^{3} x e^{log (sin x)} d x$

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Solution

$\int {cos}^{3} x e^{log (sin x)} d x$
$= \int {cos}^{3} x sin x d x$
Let $t = cos x \Rightarrow d t = - sin x d x$
$= - \int t^{3} d t$
$= - \frac{t^{4}}{4} + c$
$= - \frac{{cos}^{4} x}{4} + c$

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Evaluate ∫cos3xelog(sinx)dx

∫cos3xelog(sinx)dx=∫cos3xsinxdxLet t=cosx⇒dt=−sinxdx=−∫t3dt=−t44+c=−cos4x4+c

Evaluate $\int {cos}^{3} x e^{log (sin x)} d x$

$\int {cos}^{3} x e^{log (sin x)} d x$
$= \int {cos}^{3} x sin x d x$
Let $t = cos x \Rightarrow d t = - sin x d x$
$= - \int t^{3} d t$
$= - \frac{t^{4}}{4} + c$
$= - \frac{{cos}^{4} x}{4} + c$