Question

You only have one attempt for this problem! Evaluate the following integrals: $\int e^{2x} dx = \frac{1}{2}e^{2x} + C$ $\int cos(x/5) dx = \boxed{} + C$ $\int sin(2x) dx = \boxed{} + C$ $\int \frac{1}{7x} dx = \boxed{} + C$

          You only have one attempt for this problem!
Evaluate the following integrals:
$\int e^{2x} dx = \frac{1}{2}e^{2x} + C$
$\int cos(x/5) dx = \boxed{} + C$
$\int sin(2x) dx = \boxed{} + C$
$\int \frac{1}{7x} dx = \boxed{} + C$
        
You only have one attempt for this problem!
Evaluate the following integrals:
∫ e^2x dx = (1)/(2)e^2x + C
∫ cos(x/5) dx =  + C
∫ sin(2x) dx =  + C
∫(1)/(7x) dx =  + C

Added by Alexander S.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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You only have one attempt for this problem! Evaluate the following integrals: ∫ e^(2x) dx = ∫ cos(x/5) dx = ∫ sin(2x) dx = ∫ 1/(7x) dx = You only have one attempt for this problem! Evaluate the following integrals: ∫ e^(2x) dx = 2e^(2x) + C ∫ cos(x/5) dx = cos(x/5) + C ∫ sin(2x) dx = -1/2 cos(2x) + C ∫ 1/(7x) dx = (1/7) ln|x| + C
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Transcript

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00:01 This is problem 21 in chapter 6 .6.
00:04 This problem is asking us to find the integral of this expression.
00:09 Right now as it is, you cannot take the anti -derivative of this term.
00:16 If it was just one of these terms, it would be a lot simpler.
00:21 That since we have 2 t minus 7 to the 73rd power, there's no rule that we've learned where we can just take the integral in once easy.
00:31 Step.
00:32 So we need to use u substitution here.
00:35 The only term that we can you equal to is the one inside the 73rd power, which is 2t minus 7.
00:47 Taking the derivative of both sides, we have du is equal to 2dt.
00:54 Solving for dt to replace this in the original expression is du over 2.
01:03 Now what we have left in the integral is u to the 73rd power, multiply by du over 2...
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