Indefinite Integrals

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Example 1:

∫x2dx\int_{}^{}x^{2}dx

  • Math Solution:

∫x2dx=x33+C\int_{}^{}x^{2}dx=\frac{x^{3}}{3}+C

  • Python Code:

from sympy import symbols, integrate

x = symbols('x')
integrate(x**2, x)

Example 2:

∫(3x2+2x+1)dx\int_{}^{}\left( 3x^{2}+2x+1 \right)dx

  • Math Solution:

∫(3x2+2x+1)dx=x3+x2+x+C\int_{}^{}\left( 3x^{2}+2x+1 \right)dx=x^{3}+x^{2}+x+C

  • Python Code:

Example 3:

∫sin(x)dx\int_{}^{}sin\left( x \right)dx

  • Math Solution:

∫sin(x)dx=−cos(x)+C\int_{}^{}sin\left( x \right)dx=-cos\left( x \right)+C

  • Python Code:

Example 4:

∫cos(x)dx\int_{}^{}cos\left( x \right)dx

  • Math Solution:

∫cos(x)dx=sin(x)+C\int_{}^{}cos\left( x \right)dx=sin\left( x \right)+C

  • Python Code:

Example 5:

∫exdx\int_{}^{}e^{x}dx

  • Math Solution:

∫exdx=ex+C\int_{}^{}e^{x}dx=e^{x}+C

  • Python Code:

Example 6:

∫1xdx\int_{}^{}\frac{1}{x}dx

  • Math Solution:

∫1xdx=ln∣x∣+C\int_{}^{}\frac{1}{x}dx=ln\left| x \right|+C

  • Python Code:

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