10:[["$","title","0",{"children":"CUET Mathematics - The integral 2dxe^2x-1 is equal to: | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined The integral 2dxe^2x-1 Let u = e^2x Then du/dx = 2e^2x = 2u So dx = du/2u

2dxe^2x-1 = 2/u-1 du/2u = du/u(u-1)

1/u(u-1) = A/u + B/u-1 1 = A(u-1) + Bu Put u = 0: 1 = A(-1) A = -1 Put u = 1: 1 = B(1) B = 1 Therefore 1/u(u-1) = -1/u + 1/u-1

du/u(u-1) = -1/udu + 1/u-1du = -|u| + |u-1| + C = |u-1| - |u| + C = |u-1/u| + C

Substituting u = e^2x back: = |e^2x-1e^2x| + C Therefore, the integral equals |e^2x-1e^2x| + C"}],["$","link","2",{"rel":"manifest","href":"https://www.afterboards.in/manifest.json","crossOrigin":"$undefined"}],["$","meta","3",{"name":"keywords","content":"CUETMAT,MAT,Calculus,Integrals"}],["$","meta","4",{"name":"robots","content":"index, follow"}],["$","meta","5",{"name":"category","content":"education"}],["$","meta","6",{"name":"google-site-verification","content":"google"}],["$","meta","7",{"property":"og:title","content":"CUET Mathematics - The integral 2dxe^2x-1 is equal to: | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined The integral 2dxe^2x-1 Let u = e^2x Then du/dx = 2e^2x = 2u So dx = du/2u

2dxe^2x-1 = 2/u-1 du/2u = du/u(u-1)

1/u(u-1) = A/u + B/u-1 1 = A(u-1) + Bu Put u = 0: 1 = A(-1) A = -1 Put u = 1: 1 = B(1) B = 1 Therefore 1/u(u-1) = -1/u + 1/u-1

du/u(u-1) = -1/udu + 1/u-1du = -|u| + |u-1| + C = |u-1| - |u| + C = |u-1/u| + C

Substituting u = e^2x back: = |e^2x-1e^2x| + C Therefore, the integral equals |e^2x-1e^2x| + C"}],["$","meta","9",{"property":"og:url","content":"https://www.afterboards.in/past-year-questions/cuet-mathematics/2025/slot-13/68"}],["$","meta","10",{"property":"og:site_name","content":"AfterBoards | CUET Mathematics Preparation"}],["$","meta","11",{"property":"og:image","content":"https://www.afterboards.in/pyp/AfterBoards%20CUET%20Past%20Year%20Papers%20with%20Solutions.webp"}],["$","meta","12",{"property":"og:type","content":"website"}],["$","meta","13",{"name":"twitter:card","content":"summary_large_image"}],["$","meta","14",{"name":"twitter:site","content":"afterboards.in"}],["$","meta","15",{"name":"twitter:title","content":"CUET Mathematics - The integral 2dxe^2x-1 is equal to: | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined The integral 2dxe^2x-1 Let u = e^2x Then du/dx = 2e^2x = 2u So dx = du/2u

2dxe^2x-1 = 2/u-1 du/2u = du/u(u-1)

1/u(u-1) = A/u + B/u-1 1 = A(u-1) + Bu Put u = 0: 1 = A(-1) A = -1 Put u = 1: 1 = B(1) B = 1 Therefore 1/u(u-1) = -1/u + 1/u-1

du/u(u-1) = -1/udu + 1/u-1du = -|u| + |u-1| + C = |u-1| - |u| + C = |u-1/u| + C

Substituting u = e^2x back: = |e^2x-1e^2x| + C Therefore, the integral equals |e^2x-1e^2x| + C"}],["$","meta","17",{"name":"twitter:image","content":"https://www.afterboards.in/pyp/AfterBoards%20CUET%20Past%20Year%20Papers%20with%20Solutions.webp"}],["$","link","18",{"rel":"shortcut icon","href":"https://www.afterboards.in/favicon.ico","type":"image/x-icon","sizes":"48x48"}],["$","link","19",{"rel":"icon","href":"https://www.afterboards.in/favicon.ico","type":"image/x-icon","sizes":"48x48"}],["$","link","20",{"rel":"icon","href":"https://www.afterboards.in/icons/windows11/Square44x44Logo.altform-lightunplated_targetsize-256.png","sizes":"256x256","type":"image/png"}],["$","link","21",{"rel":"icon","href":"https://www.afterboards.in/icons/android/android-launchericon-512-512.png","sizes":"512x512","type":"image/png"}],["$","link","22",{"rel":"icon","href":"https://www.afterboards.in/icons/android/android-launchericon-192-192.png","sizes":"192x192","type":"image/png"}],["$","link","23",{"rel":"icon","href":"https://www.afterboards.in/icons/android/android-launchericon-144-144.png","sizes":"144x144","type":"image/png"}],"$L17","$L18","$L19"]

CUET Mathematics 2025 26 May Shift 2 PYQs

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