Find the Indeftnite Integral and check the result by differentiation. (5x) Step 1 To obtaln the given Integral, rewrite the Integral as dx = dx. (5x) 25 Step 2 Now apply the Power Rule for Integration to Integrate the two terms the ight side of the equation obtalned In the prevlous sbtep. dx = 5x + C (5x)2 25 Step 3 Simplify the result obtained on the right side to obtaln the Integral. Note that we use C for the constant of Integration. Sur dx = (5x)2 1. 25r 25 Step 4 To check the result, find the derivative of + C. Rewrite the expression as follows. 5x The expression is rewritten in this way beca

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Find the Indeftntte Integral and check the result by differentiation.
Step 1
To obtaln the glven Integral, rewrite the Integral as
dx.
(5x)
= xp
25
Step 2
Now apply the Power Rule for Integration to Integrate the two terms on the right side of the equation obtalned In the prevlous step.
dx = 5x
+ C
(5x)2
-1
Step 3
Simplify the result obtalned on the right side to obtain the Integral. Note that we use C for the constant of Integration.
dx =
25
Sur
1.
+ C
(5x)2
13
25.
Step 4
To check the result, find the derivative of
+ C.
Rewrite the expression as follows.
5x
The expression is rewritten Iin this way because it is easler to use the Sum Rule rather than the Quotient Rule for Differentiation.
Transcribed Image Text:Find the Indeftntte Integral and check the result by differentiation. Step 1 To obtaln the glven Integral, rewrite the Integral as dx. (5x) = xp 25 Step 2 Now apply the Power Rule for Integration to Integrate the two terms on the right side of the equation obtalned In the prevlous step. dx = 5x + C (5x)2 -1 Step 3 Simplify the result obtalned on the right side to obtain the Integral. Note that we use C for the constant of Integration. dx = 25 Sur 1. + C (5x)2 13 25. Step 4 To check the result, find the derivative of + C. Rewrite the expression as follows. 5x The expression is rewritten Iin this way because it is easler to use the Sum Rule rather than the Quotient Rule for Differentiation.
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