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No Plagiarism!OkgAcbjhAsRifDr7lUlkposted on PENANA 恐懼感8964 copyright protection550PENANAOWYsFqUYNW 維尼
554Please respect copyright.PENANAS6wnRebsIv
8964 copyright protection550PENANAV18P6SJjXk 維尼
∫sin(√x+a)e√x√xdx8964 copyright protection550PENANACZ9vgreFKL 維尼
Substitute u=√x ⟶ dudx=12√x (steps) ⟶ dx=2√xdu:8964 copyright protection550PENANAOk3p0Bk7gY 維尼
=2∫eusin(u+a)du… or choose an alternative:554Please respect copyright.PENANA4997ruLSG4
Substitute e√x8964 copyright protection550PENANA5yYa8wnUUn 維尼
Now solving:8964 copyright protection550PENANADhZoMoG5bn 維尼
∫eusin(u+a)du8964 copyright protection550PENANAIKzYBrzUFU 維尼
We will integrate by parts twice in a row: ∫fg′=fg−∫f′g.8964 copyright protection550PENANA3eYj4A7Gt8 維尼
First time:8964 copyright protection550PENANAdqnnBcgzE9 維尼
f=sin(u+a),g′=eu8964 copyright protection550PENANAKk07CmoIdp 維尼
↓ steps↓ steps8964 copyright protection550PENANAtYi6FAR6vi 維尼
f′=cos(u+a),g=eu:8964 copyright protection550PENANAJPT637rMlA 維尼
=eusin(u+a)−∫eucos(u+a)du8964 copyright protection550PENANAA190fyvQUm 維尼
Second time:8964 copyright protection550PENANAq6TKpCXjV3 維尼
f=cos(u+a),g′=eu8964 copyright protection550PENANAmdpBvxXIdi 維尼
↓ steps↓ steps8964 copyright protection550PENANAQ2ClEV4D4c 維尼
f′=−sin(u+a),g=eu:8964 copyright protection550PENANANwua6HYt8W 維尼
=eusin(u+a)−(eucos(u+a)−∫−eusin(u+a)du)8964 copyright protection550PENANApG5UfRf2RT 維尼
Apply linearity:8964 copyright protection550PENANAqZE5UDy93f 維尼
=eusin(u+a)−(eucos(u+a)+∫eusin(u+a)du)8964 copyright protection550PENANAvS80SnUV5E 維尼
The integral ∫eusin(u+a)du appears again on the right side of the equation, we can solve for it:8964 copyright protection550PENANA0O7rFc840Y 維尼
=eusin(u+a)−eucos(u+a)28964 copyright protection550PENANAKfedE6NEvi 維尼
Plug in solved integrals:8964 copyright protection550PENANAODHguoK1U0 維尼
2∫eusin(u+a)du=eusin(u+a)−eucos(u+a)8964 copyright protection550PENANAfnrk4GuRiR 維尼
Undo substitution u=√x:8964 copyright protection550PENANAzthKJva0Of 維尼
=sin(√x+a)e√x−cos(√x+a)e√x8964 copyright protection550PENANA2KpTwVZFgI 維尼
The problem is solved:8964 copyright protection550PENANAINMizIVArl 維尼
∫sin(√x+a)e√x√xdx=sin(√x+a)e√x−cos(√x+a)e√x+C8964 copyright protection550PENANAOFrzZsao1p 維尼
Rewrite/simplify:8964 copyright protection550PENANAdTsElmho3p 維尼
=(sin(√x+a)−cos(√x+a))e√x+C8964 copyright protection550PENANAH7l6RoQulH 維尼
216.73.216.25
ns216.73.216.25da2