10:[["$","title","0",{"children":"CUET Mathematics - (x^4 - x)^1/4x^5 dx is equal to | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined The integral to solve: (x^4 - x)^1/4x^5 dx Factor out x from the numerator: (x^4 - x)^1/4 = [x(x^3 - 1)]^1/4 = x^1/4 (x^3 - 1)^1/4 Rewrite the integral: x^1/4 (x^3 - 1)^1/4x^5 dx = (x^3 - 1)^1/4x^19/4 dx

Let u = 1 - 1/x^3 This can be rewritten as u = x^3 - 1/x^3, which means x^3 - 1 = x^3 u Find du: u = 1 - x^-3 du/dx = 3x^-4 du/dx = 3/x^4 dx = x^4/3 du

From x^3 - 1 = x^3 u: (x^3 - 1)^1/4 = (x^3 u)^1/4 = x^3/4 u^1/4 Substitute into the integral: x^3/4 u^1/4x^19/4 x^4/3 du = x^3/4 u^1/4 x^4x^19/4 3 du Combine powers of x in the numerator: x^3/4 x^4 = x^19/4 = x^19/4 u^1/4x^19/4 3 du = u^1/43 du

= 1/3 u^1/4 du = 1/3 u^5/45/4 + C = 1/3 4/5 u^5/4 + C = 4/15 u^5/4 + C

Substitute u = 1 - 1/x^3 back: 4/15(1 - 1/x^3)^5/4 + 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"}],["$","meta","7",{"property":"og:title","content":"CUET Mathematics - (x^4 - x)^1/4x^5 dx is equal to | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined The integral to solve: (x^4 - x)^1/4x^5 dx Factor out x from the numerator: (x^4 - x)^1/4 = [x(x^3 - 1)]^1/4 = x^1/4 (x^3 - 1)^1/4 Rewrite the integral: x^1/4 (x^3 - 1)^1/4x^5 dx = (x^3 - 1)^1/4x^19/4 dx

Let u = 1 - 1/x^3 This can be rewritten as u = x^3 - 1/x^3, which means x^3 - 1 = x^3 u Find du: u = 1 - x^-3 du/dx = 3x^-4 du/dx = 3/x^4 dx = x^4/3 du

= 1/3 u^1/4 du = 1/3 u^5/45/4 + C = 1/3 4/5 u^5/4 + C = 4/15 u^5/4 + C

Substitute u = 1 - 1/x^3 back: 4/15(1 - 1/x^3)^5/4 + C"}],["$","meta","9",{"property":"og:url","content":"https://www.afterboards.in/past-year-questions/cuet-mathematics/2025/slot-6/5"}],["$","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"}],["$","meta","15",{"name":"twitter:title","content":"CUET Mathematics - (x^4 - x)^1/4x^5 dx is equal to | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined The integral to solve: (x^4 - x)^1/4x^5 dx Factor out x from the numerator: (x^4 - x)^1/4 = [x(x^3 - 1)]^1/4 = x^1/4 (x^3 - 1)^1/4 Rewrite the integral: x^1/4 (x^3 - 1)^1/4x^5 dx = (x^3 - 1)^1/4x^19/4 dx

Let u = 1 - 1/x^3 This can be rewritten as u = x^3 - 1/x^3, which means x^3 - 1 = x^3 u Find du: u = 1 - x^-3 du/dx = 3x^-4 du/dx = 3/x^4 dx = x^4/3 du

= 1/3 u^1/4 du = 1/3 u^5/45/4 + C = 1/3 4/5 u^5/4 + C = 4/15 u^5/4 + C

Substitute u = 1 - 1/x^3 back: 4/15(1 - 1/x^3)^5/4 + C"}],"$L17","$L18","$L19","$L1a","$L1b","$L1c","$L1d","$L1e","$L1f","$L20"]

CUET Mathematics 2025 15 May Shift 2 PYQs

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