https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:integrals-ncert-new/x7ce8ca9c5869750b:untitled-1026/v/deriving-integration-by-parts-formula 2025-08-25T11:24:50.796694667Z खंडशः समाकलन का परिचय This video explains integration by parts, a technique for finding antiderivatives. It starts with the product rule for derivatives, then takes the antiderivative of both sides. By rearranging the equation, we get the formula for integration by parts. It helps simplify complex antiderivatives. Sal Khan video https://cdn.kastatic.org/googleusercontent/s7jchilivjzWyo1WUd6LdUAeuDI-JZlB0OUr55VBCRVXpPOT8pGIY0shYQ8IjZEZ9icg-iXvXgYTM7GlP5bS-HY खंडशः समाकलन का परिचय This video explains integration by parts, a technique for finding antiderivatives. It starts with the product rule for derivatives, then takes the antiderivative of both sides. By rearranging the equation, we get the formula for integration by parts. It helps simplify complex antiderivatives. https://cdn.kastatic.org/ka-youtube-converted/hO3sywF9ehg.mp4/hO3sywF9ehg.mp4 232 खंडशः समाकलन या आंशिक समाकलन (integration by parts) https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:integrals-ncert-new/x7ce8ca9c5869750b:untitled-1026/v/antiderivative-of-xcosx-using-integration-by-parts 2025-08-25T11:24:50.796694667Z खंडशः समाकलन: ∫x⋅cos(x)dx This video shows how to find the antiderivative of x*cos(x) using integration by parts. It assigns f(x)=x and g'(x)=cos(x), making f'(x)=1 and g(x)=sin(x). The formula becomes x*sin(x) - ∫sin(x)dx, which simplifies to x*sin(x) + cos(x) + C. Sal Khan video https://cdn.kastatic.org/googleusercontent/E3NVysMYbmgoUtKDT9dgqJGwTvq-Jfjp2EoHbaohLjOeNeAlHt-GHAN2-EgO1JH3NJQhT5QqDrTvEthKnsiOVRXr1Q खंडशः समाकलन: ∫x⋅cos(x)dx This video shows how to find the antiderivative of x*cos(x) using integration by parts. It assigns f(x)=x and g'(x)=cos(x), making f'(x)=1 and g(x)=sin(x). The formula becomes x*sin(x) - ∫sin(x)dx, which simplifies to x*sin(x) + cos(x) + C. https://cdn.kastatic.org/ka-youtube-converted/gi-7SUoptrg.mp4/gi-7SUoptrg.mp4 232 खंडशः समाकलन या आंशिक समाकलन (integration by parts) https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:integrals-ncert-new/x7ce8ca9c5869750b:untitled-1026/v/integral-of-ln-x 2025-08-25T11:24:50.796694667Z खंडशः समाकलन: ∫ln(x)dx This video shows how to find the antiderivative of the natural log of x using integration by parts. We rewrite the integral as ln(x) times 1dx, then choose f(x) = ln(x) and g'(x) = 1. The antiderivative is xln(x) - x + C. Sal Khan video https://cdn.kastatic.org/googleusercontent/7-zJJiDPvFeKWK6-7q-RFJPsc8nLs5rSYFPA2lMCl8wdxfpp_HAXi8yuclxEnbsfrR1yNo6yE0um6SgXzkLWj3H0 खंडशः समाकलन: ∫ln(x)dx This video shows how to find the antiderivative of the natural log of x using integration by parts. We rewrite the integral as ln(x) times 1dx, then choose f(x) = ln(x) and g'(x) = 1. The antiderivative is xln(x) - x + C. https://cdn.kastatic.org/ka-youtube-converted/Jgw_Xp1DQ0U.mp4/Jgw_Xp1DQ0U.mp4 230 खंडशः समाकलन या आंशिक समाकलन (integration by parts) https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:integrals-ncert-new/x7ce8ca9c5869750b:untitled-1026/v/integration-by-parts-twice-for-antiderivative-of-x-2-e-x 2025-08-25T11:24:50.796694667Z खंडशः समाकलन: ∫x²⋅𝑒ˣdx Integration by parts helps find antiderivatives of products of functions. We assign f(x) and g'(x) to parts of the product. Then, we find f'(x) and g(x). The formula is ∫f(x)g'(x)dx = f(x)g(x) - ∫f'(x)g(x)dx. Sometimes, we use integration by parts twice! Sal Khan video https://cdn.kastatic.org/googleusercontent/mmmbZ7tpe8KTmecRIzlOxfNHDZqoJxdPNWI-F8gCii9ipIDJuuo4LBrd5ZH1QUvln_ED8dpDzPVtXNe_RSoX6-o- खंडशः समाकलन: ∫x²⋅𝑒ˣdx Integration by parts helps find antiderivatives of products of functions. We assign f(x) and g'(x) to parts of the product. Then, we find f'(x) and g(x). The formula is ∫f(x)g'(x)dx = f(x)g(x) - ∫f'(x)g(x)dx. Sometimes, we use integration by parts twice! https://cdn.kastatic.org/ka-youtube-converted/oDFP7AUmV4o.mp4/oDFP7AUmV4o.mp4 406 खंडशः समाकलन या आंशिक समाकलन (integration by parts) https://hi.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-3/x6a634f0b79812b7f:integrals/v/integration-by-parts-of-e-x-cos-x-1 2025-08-20T07:12:56.161558644Z खंडशः समाकलन: ∫𝑒ˣ⋅cos(x)dx In the video, we learn about integration by parts to find the antiderivative of e^x * cos(x). We assign f(x) = e^x and g'(x) = cos(x), then apply integration by parts twice. The result is the antiderivative e^x * sin(x) + e^x * cos(x) / 2 + C. Sal Khan video https://cdn.kastatic.org/googleusercontent/r4fz99BvQhQWVo0oq8lK8nMhlAYxVkmNpTeMsrHllkTGnS1_Iz6qZqVvFCfIpynws4LoYgz7J5Yp5b9Ke7gDvQC- खंडशः समाकलन: ∫𝑒ˣ⋅cos(x)dx In the video, we learn about integration by parts to find the antiderivative of e^x * cos(x). We assign f(x) = e^x and g'(x) = cos(x), then apply integration by parts twice. The result is the antiderivative e^x * sin(x) + e^x * cos(x) / 2 + C. https://cdn.kastatic.org/ka-youtube-converted/H9RPI2d-H6c.mp4/H9RPI2d-H6c.mp4 437 खंडशः समाकलन या आंशिक समाकलन (integration by parts) https://hi.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-3/x6a634f0b79812b7f:integrals/e/integration-by-parts 2025-06-25T04:37:22.958747522Z खंडशः समाकलन या आंशिक समाकलन (integration by parts) आंशिक समाकलन (Integration by Parts) विधि का उपयोग करके अनिश्चित समाकलनों (indefinite integrals) के प्रश्नों का अभ्यास करें। Bill Scott exercise