Indefinite Integrals

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Example 1:

$$\int_{}^{}x^{2}dx$$

• Math Solution:

$$\int_{}^{}x^{2}dx=\frac{x^{3}}{3}+C$$

• Python Code:

from sympy import symbols, integrate

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

Example 2:

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

• Math Solution:

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

• Python Code:

from sympy import symbols, integrate

x = symbols('x')
integrate(3*x**2 + 2*x + 1, x)

Example 3:

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

• Math Solution:

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

• Python Code:

from sympy import symbols, integrate, sin

x = symbols('x')
integrate(sin(x), x)

Example 4:

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

• Math Solution:

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

• Python Code:

from sympy import symbols, integrate, cos

x = symbols('x')
integrate(cos(x), x)

Example 5:

$$\int_{}^{}e^{x}dx$$

• Math Solution:

$$\int_{}^{}e^{x}dx=e^{x}+C$$

• Python Code:

from sympy import symbols, integrate, exp

x = symbols('x')
integrate(exp(x), x)

Example 6:

$$\int_{}^{}\frac{1}{x}dx$$

• Math Solution:

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

• Python Code:

from sympy import symbols, integrate

x = symbols('x')
integrate(1/x, x)