What is the integral of cos(x)+(x^2+1)^7*2x ?

The integral of cos(x)+(x^2+1)^7*2x is sin(x)+1/8 (x^2+1)^8+C

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integral of cos(x)+(x^2+1)^7*2x

\int cos (x) + (x^{2} + 1)^{7} \cdot 2 x d x

sin (x) + \frac{1}{8} (x^{2} + 1)^{8} + C

Solution steps

\int cos (x) + (x^{2} + 1)^{7} \cdot 2 x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int cos (x) d x + \int (x^{2} + 1)^{7} \cdot 2 x d x

\int cos (x) d x = sin (x)

\int (x^{2} + 1)^{7} \cdot 2 x d x = \frac{1}{8} (x^{2} + 1)^{8}

= sin (x) + \frac{1}{8} (x^{2} + 1)^{8}

Add a constant to the solution

= sin (x) + \frac{1}{8} (x^{2} + 1)^{8} + C

\frac{d y}{d x}, ln (x y^{3}) = x y

\int \frac{tan ^{3} ( ln ( x ) )}{2 x} d x

f (x) = cos^{5} (x)

arcsec (\frac{1}{4 t ^{5}})

n = 0 \sum \infty \frac{z ^{n}}{n ^{2}}

What is the integral of cos(x)+(x^2+1)^7*2x ?
The integral of cos(x)+(x^2+1)^7*2x is sin(x)+1/8 (x^2+1)^8+C