Integral of cos^3(x)sin^4(x) (substitution)

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Integral of cos^3(x)sin^4(x) - How to integrate it step by step using the substitution method!

🚶 𝐒𝐭𝐞𝐩𝐬
00:00 Rewrite expression
00:16 Use the 1=sin^2(x)+cos^2(x) trig identity
00:56 Substitution: u=sin(x)
01:04 Differentiate in both sides
01:08 Substitute sin(x) and cos(x)dx
01:24 Rewrite expression
01:33 Integrate u^4 and u^6
01:47 Undo substitution: u in terms of x
02:01 Add integration constant +C
02:08 Final answer!

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► Integration by parts

► Integration by substitution

► Integration by trig substitution

► Integration by Weierstrass substitution

► Integration by partial fraction decomposition

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👋 Follow @integralsforyou for a daily integral 😉

𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐢𝐨𝐧 𝐦𝐞𝐭𝐡𝐨𝐝𝐬 𝐩𝐥𝐚𝐲𝐥𝐢𝐬𝐭
► Integration by parts

► Integration by substitution

► Integration by trig substitution

► Integration by Weierstrass substitution

► Integration by partial fraction decomposition


𝐅𝐨𝐥𝐥𝐨𝐰 𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬 𝐅𝐨𝐫𝐘𝐨𝐮
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IntegralsForYou
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Solution:
∫cos³(x)*sin^4(x)*dx =
—————————————————————————
Substitution: u = sin(x) du/dx = cos(x) dx = du/cos(x)
————————————————————————
= ∫cos²(x)*u^4*du = ∫(1-sin²(x))*u^4*du = ∫(1-u²)*u^4*du
= ∫(u^4-u^6)*du = u^5/5-u^7/7+C = sin^5(x)/5-sin^7(x)/7+C

Sample by deriving:
[sin^5(x)/5-sin^7(x)/7+C]’ =
= sin^4(x)*cos(x)*[1-sin²(x)] = sin^4(x)*cos³(x) all o.k.

gelbkehlchen
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Integral
(arcsin(sqrt(x)) / (sqrt(1-x)) dx
Thank you!

kahahdmajaksh
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cool channel to relax to
why not make multidimensional integrals too? perhaps some stokes or gauss law or volume integrals

bebarshossny
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Can u do this one plz:
Int 3^sinx/1+3^sinx dx

T-Ko
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Integral
(sqrt (4*x-x^2-3)) / (x-2)^2 dx

kahahdmajaksh
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hello can you help me solving these by geomtric series sum
1+(-2)^n/4^n n=1

battomisaadi
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Hey, maybe you can do cos(5x)^3sin(4x)^5?

glorymanheretosleep