How do you integrate $\int (3 - x) 7^{{(3 - x)}^{2}} d x$ $int (3-x)7^((3-x) ^2)dx$ ?

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How do you integrate $\int (3 - x) 7^{{(3 - x)}^{2}} d x$ $int (3-x)7^((3-x) ^2)dx$ ?

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Answer 1 · 2016-12-21T13:27:16

$\int (3 - x) 7^{{(3 - x)}^{2}} d x = - \frac{7^{{(3 - x)}^{2}}}{2 ln 7} + C$ $int (3-x)7^((3-x)^2)dx=-(7^((3-x)^2))/(2ln7)+C$

Explanation:

Substitute $t = {(3 - x)}^{2}$ $t=(3-x)^2$ , $d t = - 2 (3 - x) d x$ $dt=-2(3-x)dx$ , and consider that $7^{α} = e^{α ln 7}$ $7^alpha= e^(alphaln7)$ :

$\int (3 - x) 7^{{(3 - x)}^{2}} d x = - \frac{1}{2} \int e^{ln 7 t} d t = - \frac{1}{2} ln 7 e^{ln 7 t} + C = - \frac{7^{{(3 - x)}^{2}}}{2 ln 7} + C$ $int (3-x)7^((3-x)^2)dx= -1/2int e^(ln7t)dt=-1/2ln7e^(ln7t)+C=-(7^((3-x)^2))/(2ln7)+C$

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How do you integrate $\int (3 - x) 7^{{(3 - x)}^{2}} d x$ $int (3-x)7^((3-x) ^2)dx$ ?

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Explanation:

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How do you integrate $\int (3 - x) 7^{{(3 - x)}^{2}} d x$ $int (3-x)7^((3-x) ^2)dx$ ?