Question
Evaluate the integral
−3e2xx+6e2x+C,C∈R
Evaluate
∫−32xe2xdx
Use the property of integral ∫kf(x)dx=k∫f(x)dx
−32×∫xe2xdx
Prepare for integration by parts
u=xdv=e2xdx
Calculate the derivative
More Steps

Calculate the derivative
u=x
Evaluate the derivative
du=x′dx
Evaluate the derivative
du=1dx
Simplify the expression
du=dx
du=dxdv=e2xdx
Evaluate the integral
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Evaluate the integral
dv=e2xdx
Evaluate the integral
∫1dv=∫e2xdx
Evaluate the integral
v=2e2x
du=dxv=2e2x
Substitute u=x、v=2e2x、du=dx、dv=e2xdx for ∫udv=uv−∫vdu
−32(x×2e2x−∫1×2e2xdx)
Calculate
−32(2xe2x−∫2e2xdx)
Calculate
−32×2xe2x−(−32×∫2e2xdx)
Evaluate
−32×2xe2x+32×∫2e2xdx
Evaluate the integral
More Steps

Evaluate the integral
32×∫2e2xdx
Rewrite the expression
32×∫21e2xdx
Use the property of integral ∫kf(x)dx=k∫f(x)dx
32×21×∫e2xdx
Multiply the numbers
More Steps

Evaluate
32×21
Reduce the numbers
31×1
Multiply the numbers
31
31×∫e2xdx
Use the property of integral ∫eax=a1eax
31×21e2x
Multiply the terms
31×2e2x
Multiply the terms
3×2e2x
Multiply the terms
6e2x
−32×2xe2x+6e2x
Calculate
More Steps

Multiply the terms
−32×2xe2x
Cancel out the common factor 2
−31xe2x
Multiply the terms
−3xe2x
−3xe2x+6e2x
Simplify the expression
−3e2xx+6e2x
Solution
−3e2xx+6e2x+C,C∈R
Show Solution
