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Question
\int \left(3x^{2}+4x\right) dx
Evaluate the integral
x^{3}+2x^{2}+C,C \in \mathbb{R}
Evaluate
\int \left(3x^{2}+4x\right) dx
\text{Use the property of integral }\int f(x) \pm g(x) dx=\int f(x) dx \pm \int g(x) dx
\int 3x^{2} dx+\int 4x dx
Evaluate the integral
More Steps
Evaluate
\int 3x^{2} dx
\text{Use the property of integral }\int kf(x) dx=k\int f(x) dx
3\times \int x^{2} dx
\text{Use the property of integral }\int x^{n} dx = \frac{x^{n+1}}{n+1}
3\times \frac{x^{2+1}}{2+1}
Add the numbers
3\times \frac{x^{3}}{2+1}
Add the numbers
3\times \frac{x^{3}}{3}
\text{Cancel out the common factor }3
1\times x^{3}
Multiply the terms
x^{3}
x^{3}+\int 4x dx
Evaluate the integral
More Steps
Evaluate
\int 4x dx
\text{Use the property of integral }\int kf(x) dx=k\int f(x) dx
4\times \int x dx
\text{Use the property of integral }\int x^{n} dx = \frac{x^{n+1}}{n+1}
4\times \frac{x^{1+1}}{1+1}
Add the numbers
4\times \frac{x^{2}}{1+1}
Add the numbers
4\times \frac{x^{2}}{2}
\text{Cancel out the common factor }2
2x^{2}
x^{3}+2x^{2}
Solution
x^{3}+2x^{2}+C,C \in \mathbb{R}
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