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Find the integral $\int\left(7x^3+\cos\left(x\right)^4\right)dx$

Step-by-step Solution

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Final Answer

$\frac{7}{4}x^{4}+\frac{3}{8}x+\frac{3}{16}\sin\left(2x\right)+\frac{\cos\left(x\right)^{3}\sin\left(x\right)}{4}+C_0$
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Step-by-step Solution

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Expand the integral $\int\left(7x^3+\cos\left(x\right)^4\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

$\int7x^3dx+\int\cos\left(x\right)^4dx$

Learn how to solve product rule of differentiation problems step by step online.

$\int7x^3dx+\int\cos\left(x\right)^4dx$

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Learn how to solve product rule of differentiation problems step by step online. Find the integral int(7x^3+cos(x)^4)dx. Expand the integral \int\left(7x^3+\cos\left(x\right)^4\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int7x^3dx results in: \frac{7}{4}x^{4}. The integral \int\cos\left(x\right)^4dx results in: \frac{\cos\left(x\right)^{3}\sin\left(x\right)}{4}+\frac{3}{4}\left(\frac{1}{2}x+\frac{1}{4}\sin\left(2x\right)\right). Gather the results of all integrals.

Final Answer

$\frac{7}{4}x^{4}+\frac{3}{8}x+\frac{3}{16}\sin\left(2x\right)+\frac{\cos\left(x\right)^{3}\sin\left(x\right)}{4}+C_0$

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Solve integral of (7x^3+cosx^4)dx using basic integralsSolve integral of (7x^3+cosx^4)dx using u-substitutionSolve integral of (7x^3+cosx^4)dx using integration by partsSolve integral of (7x^3+cosx^4)dx using tabular integration

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Function Plot

Plotting: $\frac{7}{4}x^{4}+\frac{3}{8}x+\frac{3}{16}\sin\left(2x\right)+\frac{\cos\left(x\right)^{3}\sin\left(x\right)}{4}+C_0$

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0
a
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f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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Main Topic: Product Rule of differentiation

The product rule is a formula used to find the derivatives of products of two or more functions. It may be stated as $(f\cdot g)'=f'\cdot g+f\cdot g'$

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