✓x+1/✓x find the integration
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The best way to solve this kind of integral is by u-substitution of 1+
and using the sum rule and power rule for the rest.
Substitute =1+
. compute (1+)=1
, so =
. Since we can express =+1–1
, so we have ∫(−1)√
We can express √=12
, so: ∫(−1)12
Distribute the parenthesis: =∫12−12⇒∫32−12
Use the sum rule: ∫32−∫12
So now we solve the integral term by term by using the power rule for each term.
Solving for ∫32=32+132+1⇒2525
Solving for ∫12=12+112+1⇒2323
Plug in solved integrals: 2525−2323
Undo substitution of =+1
: =2(+1)525−2(+1)323
And that is all there is to it. Add the constant of integration to finish the solution:
=2(+1)525−2(+1)323+
and using the sum rule and power rule for the rest.
Substitute =1+
. compute (1+)=1
, so =
. Since we can express =+1–1
, so we have ∫(−1)√
We can express √=12
, so: ∫(−1)12
Distribute the parenthesis: =∫12−12⇒∫32−12
Use the sum rule: ∫32−∫12
So now we solve the integral term by term by using the power rule for each term.
Solving for ∫32=32+132+1⇒2525
Solving for ∫12=12+112+1⇒2323
Plug in solved integrals: 2525−2323
Undo substitution of =+1
: =2(+1)525−2(+1)323
And that is all there is to it. Add the constant of integration to finish the solution:
=2(+1)525−2(+1)323+
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