Question
Evaluate the integral
−49x4−3x+C,C∈R
Evaluate
∫3(−x3−2x2×x−1)dx
Multiply
More Steps

Multiply the terms
−2x2×x
Multiply the terms with the same base by adding their exponents
−2x2+1
Add the numbers
−2x3
∫3(−x3−2x3−1)dx
Subtract the terms
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Evaluate
−x3−2x3−1
Subtract the terms
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Evaluate
−x3−2x3
Collect like terms by calculating the sum or difference of their coefficients
(−1−2)x3
Subtract the numbers
−3x3
−3x3−1
∫3(−3x3−1)dx
Multiply the terms
More Steps

Evaluate
3(−3x3−1)
Apply the distributive property
3(−3x3)−3×1
Multiply the numbers
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Evaluate
3(−3)
Multiplying or dividing an odd number of negative terms equals a negative
−3×3
Multiply the numbers
−9
−9x3−3×1
Any expression multiplied by 1 remains the same
−9x3−3
∫(−9x3−3)dx
Rewrite the expression
∫−3(3x3+1)dx
Use the property of integral ∫kf(x)dx=k∫f(x)dx
−3×∫(3x3+1)dx
Use the property of integral ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx
−3(∫3x3dx+∫1dx)
Calculate
−3×∫3x3dx−3×∫1dx
Evaluate the integral
More Steps

Evaluate
−3×∫3x3dx
Use the property of integral ∫kf(x)dx=k∫f(x)dx
−3×3×∫x3dx
Multiply the numbers
−9×∫x3dx
Use the property of integral ∫xndx=n+1xn+1
−9×3+1x3+1
Simplify
More Steps

Evaluate
3+1x3+1
Add the numbers
3+1x4
Add the numbers
4x4
−9×4x4
Multiply the terms
−49x4
−49x4−3×∫1dx
Use the property of integral ∫kdx=kx
−49x4−3x
Solution
−49x4−3x+C,C∈R
Show Solution
