What is $\int (4 x^{3} + cos x) d x$ $\int ( 4x ^ { 3} + \cos x ) d x$ ?

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What is $\int (4 x^{3} + cos x) d x$ $\int ( 4x ^ { 3} + \cos x ) d x$ ?

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Answer 1 · 2018-02-07T16:43:50

$x^{4} + sin x$ $x^4+sinx$

Explanation:

$\int a + b$ $inta+b$ = $\int a$ $int a$ + $\int b$ $intb$
$\int 4 x^{3} d x$ $int4x^3dx$ $+$ $+$ $\int cos x d x$ $intcosxdx$
use the reverse power rule to integrate $4 x^{3}$ $4x^3$
$\int m x^{n}$ $intmx^n$ = $\int \frac{m x^{n + 1}}{n + 1}$ $int(mx^(n+1))/(n+1)$
since $\frac{d}{d x} sin x = cos x$ $d/dx sinx=cosx$ , you can reverse it to integrate $cos x$ $cosx$
so, $\int 4 x^{3} d x$ $int4x^3dx$ $+$ $+$ $\int cos x d x$ $intcosxdx$
= $4 \frac{x^{4}}{4}$ $4(x^4)/4$ + $sin x$ $sinx$
= $x^{4} + sin x$ $x^4+sinx$

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What is $\int (4 x^{3} + cos x) d x$ $\int ( 4x ^ { 3} + \cos x ) d x$ ?

1 Answer

Explanation:

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What is $\int (4 x^{3} + cos x) d x$ $\int ( 4x ^ { 3} + \cos x ) d x$ ?