10:[["$","title","0",{"children":"CUET Mathematics - (1/log_e t - 1/(log_e t)^2) dt is equal to | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined Given integral: (1/_e t - 1/(_e t)^2) dt The integrand can be recognized as the derivative of t/_e t.

Consider differentiating t/_e t using the quotient ru<=. For y = u/v, the derivative is dy/dt = v du/dt - u dv/dtv^2 Here, u = t and v = _e t So du/dt = 1 and dv/dt = 1/t

d/dt(t/_e t) = (_e t)(1) - (t)(1/t)(_e t)^2 = _e t - 1/(_e t)^2 = _e t/(_e t)^2 - 1/(_e t)^2 = 1/_e t - 1/(_e t)^2

This matches the given integrand exactly. Therefore: (1/_e t - 1/(_e t)^2) dt = t/_e t + 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"}],["$","meta","7",{"property":"og:title","content":"CUET Mathematics - (1/log_e t - 1/(log_e t)^2) dt is equal to | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined Given integral: (1/_e t - 1/(_e t)^2) dt The integrand can be recognized as the derivative of t/_e t.

Consider differentiating t/_e t using the quotient ru<=. For y = u/v, the derivative is dy/dt = v du/dt - u dv/dtv^2 Here, u = t and v = _e t So du/dt = 1 and dv/dt = 1/t

d/dt(t/_e t) = (_e t)(1) - (t)(1/t)(_e t)^2 = _e t - 1/(_e t)^2 = _e t/(_e t)^2 - 1/(_e t)^2 = 1/_e t - 1/(_e t)^2

This matches the given integrand exactly. Therefore: (1/_e t - 1/(_e t)^2) dt = t/_e t + C"}],["$","meta","9",{"property":"og:url","content":"https://www.afterboards.in/past-year-questions/cuet-mathematics/2025/slot-2/4"}],["$","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"}],["$","meta","15",{"name":"twitter:title","content":"CUET Mathematics - (1/log_e t - 1/(log_e t)^2) dt is equal to | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined Given integral: (1/_e t - 1/(_e t)^2) dt The integrand can be recognized as the derivative of t/_e t.

Consider differentiating t/_e t using the quotient ru<=. For y = u/v, the derivative is dy/dt = v du/dt - u dv/dtv^2 Here, u = t and v = _e t So du/dt = 1 and dv/dt = 1/t

d/dt(t/_e t) = (_e t)(1) - (t)(1/t)(_e t)^2 = _e t - 1/(_e t)^2 = _e t/(_e t)^2 - 1/(_e t)^2 = 1/_e t - 1/(_e t)^2

This matches the given integrand exactly. Therefore: (1/_e t - 1/(_e t)^2) dt = t/_e t + 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"}],["$","link","21",{"rel":"icon","href":"https://www.afterboards.in/icons/android/android-launchericon-512-512.png","sizes":"512x512","type":"image/png"}],"$L17","$L18","$L19","$L1a","$L1b"]

CUET Mathematics 2025 13 May Shift 2 PYQs

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