integral of x^4

{ "query": { "display": "integral $$x^{4}$$", "symbolab_question": "PRE_CALC#integral x^{4}" }, "solution": { "level": "PERFORMED", "subject": "Calculus", "topic": "Integrals", "subTopic": "Indefinite Integrals", "default": "\\frac{x^{5}}{5}+C", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\int\\:x^{4}dx=\\frac{x^{5}}{5}+C$$", "input": "\\int\\:x^{4}dx", "steps": [ { "type": "interim", "title": "Apply the Power Rule", "input": "\\int\\:x^{4}dx", "result": "=\\frac{x^{5}}{5}", "steps": [ { "type": "step", "primary": "Apply the Power Rule: $$\\int{x^{a}}dx=\\frac{x^{a+1}}{a+1},\\:\\quad\\:a\\neq{-1}$$", "result": "=\\frac{x^{4+1}}{4+1}" }, { "type": "interim", "title": "Simplify $$\\frac{x^{4+1}}{4+1}:{\\quad}\\frac{x^{5}}{5}$$", "input": "\\frac{x^{4+1}}{4+1}", "steps": [ { "type": "step", "primary": "Add the numbers: $$4+1=5$$", "result": "=\\frac{x^{5}}{5}" } ], "meta": { "solvingClass": "Solver", "interimType": "Algebraic Manipulation Simplify Title 1Eq" } }, { "type": "step", "result": "=\\frac{x^{5}}{5}" } ], "meta": { "interimType": "Power Rule Top 0Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7l7+Hp9GxvB/5I+4/5L7s792bwOWB9XLV4lUXfjhDNcao/JI5bBgpgExN510TA5cyodqSCYnUP+KiNK7E2zlYiE/QYMzREewyYhmRoDar7oesKQBqfZltZgKEVL7oPcXqgQUxJPyUNnGfVirkcwpVOw39JmBCMfU6hqFWM4cbYeuPws1TZ9p9GAZMOucM4Sei" } }, { "type": "step", "primary": "Add a constant to the solution", "result": "=\\frac{x^{5}}{5}+C", "meta": { "title": { "extension": "If $$\\frac{dF\\left(x\\right)}{dx}=f\\left(x\\right)$$ then $$\\int{f\\left(x\\right)}dx=F\\left(x\\right)+C$$" } } } ], "meta": { "solvingClass": "Integrals", "practiceLink": "/practice/integration-practice", "practiceTopic": "Integrals" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "y=\\frac{x^{5}}{5}+C" }, "showViewLarger": true } }, "meta": { "showVerify": true } }