Solve ∫ (from 0 to 1) of (x+3)e^x wrt x=a+text{bevoi}a

$$\int _ { 0 } ^ { 1 } ( x + 3 ) e ^ { x } d x = a + \text { be voi } a$$

Solve for a

$$a=\frac{3e-2}{eibov+1}$$

$$o=0\text{ or }v=0\text{ or }b\neq \frac{i}{eov}$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+3 by e^{x}.

$$\int _{0}^{1}xe^{x}+3e^{x}\mathrm{d}x=a+bevoia$$

Swap sides so that all variable terms are on the left hand side.

$$a+bevoia=\int _{0}^{1}xe^{x}+3e^{x}\mathrm{d}x$$

Combine all terms containing a.

$$\left(1+bevoi\right)a=\int _{0}^{1}xe^{x}+3e^{x}\mathrm{d}x$$

The equation is in standard form.

$$\left(eibov+1\right)a=3e-2$$

Divide both sides by 1+ibevo.

$$\frac{\left(eibov+1\right)a}{eibov+1}=\frac{3e-2}{eibov+1}$$

Dividing by 1+ibevo undoes the multiplication by 1+ibevo.

$$a=\frac{3e-2}{eibov+1}$$

Solve for b

$$\left\{\begin{matrix}b=\frac{i\left(a+2-3e\right)}{eaov}\text{, }&a\neq 0\text{ and }o\neq 0\text{ and }v\neq 0\\b\in \mathrm{R}\text{, }&a=3e-2\text{ and }\left(o=0\text{ or }v=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+3 by e^{x}.

$$\int _{0}^{1}xe^{x}+3e^{x}\mathrm{d}x=a+bevoia$$

Swap sides so that all variable terms are on the left hand side.

$$a+bevoia=\int _{0}^{1}xe^{x}+3e^{x}\mathrm{d}x$$

Subtract a from both sides.

$$bevoia=\int _{0}^{1}xe^{x}+3e^{x}\mathrm{d}x-a$$

The equation is in standard form.

$$eiaovb=-a+3e-2$$

Divide both sides by ievoa.

$$\frac{eiaovb}{eiaov}=\frac{-a+3e-2}{eiaov}$$

Dividing by ievoa undoes the multiplication by ievoa.

$$b=\frac{-a+3e-2}{eiaov}$$

Divide 3e-2-a by ievoa.

$$b=-\frac{i\left(-a+3e-2\right)}{eaov}$$